Both are important but, in my opinion, good writing can save a cliche plot, but a fantastic, original storyline doesn't matter if the writing's too painful to read.
(Of course, they're both a continuum and you need at least a base level of both to make a readable book, but for me, writing skill is more important than story)
IMO if it's written well enough, the skill becomes the story. Books can get pretty abstract about if story really needs to be there. Kind of like how art doesn't need to be of anything subjective at all. Kinda depends what you're looking for, and if you find yourself in a story-less novel or short story, like that is kind of the point. Personally I've enjoyed both, but only if it's written well.
It doesn't matter how good the ideas in your head are if you can't communicate them.
The longer answer is that it's about the sum of the parts. It's called "storytelling" because it's the marriage of the story and the telling that create the meaningful experience for the reader. This is true for any media, not just writing, of course! I think it's also go to be aware that it's not really as straight forward as "good or bad" for either the story or the writing. Both story and writing can be farther broken down into many components with the creator being better at some things than others.
As SleepingPoppy already said, it's about storytelling. A good storyteller can make people interested in any story. But if the story is bad, people will stop listening/reading.
I'd say it's more important to have the skills to tell a story than the story itself because a good story in the "wrong" hands will fail. Movies are a perfect example of this; many awesome stories that already succeeded as books fail because they couldn't tell the story effectively.
I was thinking about adaptations when I was writing my response! The ability to adapt a story to the particular medium is it's own artform/skill! XD
I will say both but only if "talent" is included under the writing skill umbrella. I love reading fairytale adaptations, but the problem is that the stories tend to feel "recycled". I've read countless Cinderella adaptations where the MC is abused by her stepfamily only to be rescued by the prince. But in "Ella Enchanted", the author turns the familiar story on its ear and creates an entirely unique premise on a classic tale. I watched a modern adaptation of "Pride and Prejudice" that wasn't the best written script, but it nails female friendships and the pressures of finding love as an adult.
It's a balancing act.
I see that the majority chose writing over story skills (or 50/50).
I have a question for everyone who prefers writing skills: 'beside spelling and grammar, what elements (dialogues, structure, word choices, detailed descriptions or to the point,...) do you see as (very) important when writing or reading a story, and why?'
Writing skill.
It's 2021 and honestly no plot or story is completely original but what is original on most cases, when it comes to a good writer, is how they execute that narrative and plot in a unique way.
Maybe its how the characters talk to one another, maybe its how the plot progresses; whatever it is, writing helps excel a seemingly simple story to something more and that takes skill.
A good story is icing on the cake, it is cool to look at and if done well can be impressive as hell. But at the end of the day, the quality of a book is measured by it's mushy soft interior and the flavor of the creamy filling... Not the icing by itself.
It is worth noting first that those things carry different value depending on the media. When we are dealing with comic books, operas or tv shows, there are many more moving parts to it, those are instances where the writing is actually the icing and the visuals and presentation are the filling... For instance I care very little for the plot of naruto, but the fights look impressively detailed and well animated, and just because I want to catch EVEN MORE FLAK, JOJO is an example of how an art carries the whole manga on it's shoulders with a very... eh... plot.
On a novel however, these things are entwineed, the quality of writing IS BOTH THE FILLING AND THE ICING, a simple cake that takes a lot to balance properly.
Here is an easy way to show you... Pick you favorite book, any one.... Now remove pretty much every character stylization, take all scenery descriptions and replace them with their most basic, and write it in the most accurate formal language you can... And now, you know what makes your favorite book interesting right?
A good story is just an idea, and ideas without execution are pretty damn useless in the grand scheme of things... Not saying you cannot have a stellar epiphany of the greatest story every told, but for a novel to suceed you to have the words to MAKE IT stellar.
Now what makes for 'writting skill' varies...
Writing is an art form there are many things you can learn about it and improve, a movie maker would learn 'shot composition' while you as a novelist learn 'scening', a traditional artist learns 'anatomy' like you would learn how to describe movement.
Generally speaking, descriptions are a pretty damn good starting point for any writer, trying to narrate the same scene multiple times using different words to stimulate different senses and invoke different feelings on the reader.
Next i'd say story structure, learn to create the 'Rube goldberg' machine that connects your plot together. Wether you want to plan the muder from the start and then write around it, or you want to just find out along your characters how the muder took place is what makes of breaks a plot.
The flair added in to make it better, it is the thing we call characterization, but do not underestimate the value of it, characterization is what keeps characters consistant and their personas matching the world they live in... Remember it is fantasy for us but real for them, so sure you think dragons are cool, but if they burn down the MCs village and he is just fine with them, that's sort of... Off...
Finally stylization, learn different vocabularies, regionalism, some psychology might also help, and try and make things more unique, like a painter carefully selecting each color on the pallet thinking ahead to carefully match them.
Other details are exclusively up to you, but remember, each part of this process ADDS ON to the previous, none of these is enough to carry a story by themselves, so the more steps you add the more you have to keep track off.
I don't imagine you'd get anywhere without some amount of both.
What if it's the most interesting plot you've ever read, but it reads like shit because the author can't grasp basic grammar or flow or transitions are terrible or they just bounce back and forth all the time or they don't know how to split sentences when they're obviously going on for too long without giving the reader a chance for breath?
What if the person is an expert in the above, but their fucking story is dumb?
I suspect a really great yarn can survive a less than sterling writing style & a really good story-teller can make an everyday event rather riveting. So, I'm not sure one can state categorically that one is more important than the other.
Having both good plot and writing skills is preferable, but if I have to choose one: writing skills. I've been disappointed too many times by being lured in by a summary and promises of something that's right up my alley, only to have the story handled and delivered in amazingly bad ways. There will be constant grammar and spelling errors, stiff dialogue, and an inability to maintain their own characterization. Or the prose are written in such a way that you can instantly imagine them being read out loud for children's storytime in an obnoxious voice.
Dialogues and structure.
Structure is necessary to keep everything in order and make sense. Dialogue is an important part because it's when the author "steps back" and lets the characters be themselves. This will put to test if the story is more than the views of the author.
Word choices are the least important thing. The message behind those words it's what matters, not the words themselves.
Both are important, however, a story is communicating with the reader and if it is communicated poorly, the story and plot will be lost in translation.
Writing skill and style of prose.
I have read a lot of fast-paced stories with a lot of things happening, but have snored through them because they've been written poorly, or the prose just doesn't express the emotions of the scenes.
But I have also read one short story that is literally just a boat ride down a river. But the writing gave me the tone, the characters' inner emotions, and the melancholy of the boat ride and its symbolism of their drifting lives; all delivered in prose that flowed like silk and elicited all kinds of emotions within me.
Plot is like a list of facts that are laid out for us, the audience. But what makes it all coalesce into the story we care about is the way it is delivered.
Ohhhh man, this is definitely one of those "the chicken or the egg" questions ahaha.
I think in an ideal world, the answer would be both -- interesting plot written beautifully.
In the real world, however, I will take an interesting story with flawed writing any day over bland purple prose. Especially after the 9-to-5 grind of adulting, at the end of a long day, I won't have the brainpower to whip out the dictionary every other sentence just to understand a 3-paragraph description of...a door, or something.
I read one such (traditionally published) book a while ago, which was absolutely beautifully written. Stunning. The characters and story, on the other hand...were ultimately disappointing.
Conversely, last summer I binged an (online published) teen fiction book which I normally am not attracted to. It was so funny, and written with so much heart, and even though the writing wasn't extraordinary or perfect, I enjoyed it immensely.
So, I would say, a fair balance of decent writing and gripping story is the best combination!
Yes! I agree with @alcoholandcaffeine
My instant answer would be "good writing of course!"
But if I'm to be honest with myself - truly honest - I would take good plot with decent writing over bad plot with amazing writing.
I say "decent" because I still need to understand what's going on. If you have the basic grammar down I won't complain.
I adore purple prose because it truly is an art form but in words. It can paint such a beautiful picture for sure. But 300 pages of purple prose? I will pass because after my 9-5 job my brain is fried. (Purple prose works best for me in a short story)
If I were to choose, a better plot is always better than the writing style/skill.
For example, this sign:
I didn't see the repeated "the," and I only saw it after it was pointed out to me. Your brain fills in the gaps, and I tend to gloss over mistakes:
These are extreme examples, but they get the point across. As long as the writing is unobtrusive and communicates the plot effectively, it'll most likely be OK. Work on the plot first, then fix writing issues while you're editing. Even better, have someone else read the writing first, and have them give feedback.
This is pretty late but...
For me, it's both the writing skill (mainly focusing on grammar and structure) and story plot. There were a few novels I've come across on tapas that interested me based on the synopsis and overall plot. But what made me lose interest quickly was the lack of structure and poor grammar.
Like @Moctemma mentioned, structure is key in getting your message across. Yet, if what you're trying to convey to the reader is all over the place, as a reader, it's hard to follow. I know for sure that I won't bother trying to follow a story where I have no idea what's going on. The safest bet is to have someone else read your work after you've proofread it multiple times (even then, there's still going to be grammar mistakes xD But at least they'll be minor). 
