Personally, it depends a lot on the way the site is set up (and if it is beneficial to the enjoyment of the comic). If your comic has a unique layout or special media effects, then you absolutely should consider having a unique site for it, provided you have the ability, time, and/or money to make it work well. If you've got a big world with lots of characters, it can be neat to set everything up on its own site just to have some world info and character pages and such.
I don't want to sound like an ass for saying this, but I have found some attempts at self-hosting detrimental to my enjoyment of the comic. 90% of the time I will if the site is ugly (as in, looks like it came out of 1991 ugly).
There are some current web design trends that would be great for webcomic-making! The first thing I thought of was parallax scrolling; here's a pretty good example I found through a quick google search. The added level of interactivity also can help engage your reader into the story through clickables, etc. Keep in mind cross-platform compatibility though!
Also I really, really love it when creators allow pages in a chapter to be loaded in 'seamlessly' through some nice CSS/JS/Angular/whatever it takes. I find the flashy load-reloads between pages on a lot of sites breaks the flow of the story a little, so it's always a nice option to have if you can put it in place.
Best of luck!