Neither.
As everything it needs to be used with parsimony and only when it makes sense.

I'm ok with both your understanding and the critics.
It's difficult to imagine how emotions would not influence a build-in power (or magic), however, using this for an easy win... nope.

One can probably keep things more interesting by keeping the effects mild (not enough to change the outcome all by themselves; emotion effect is only a parameter among others), realistically balanced (some emotions will have a positive effect, some a negative effect, and some an effect that may end up positive or negative depending on situation and environment) and taking in account interactions between emotions (you don't necessarily only feel one single emotion at the same time an the interaction will affect the powers too, probably in a novel way compared to 'pure' emotions).

I don't think to really "can" separate emotions from superpower/ special abilities. Emotions are one of the elements that make us human. Even if you have a character who can manipulate people's emotions, they could easily be overwhelmed by everyone's emotional state so they can't function. There could also be a moral dilemma that's preventing the character from using their ability. One character I know has the ability to compel people into doing whatever she wants. The people she works with won't make eye contact with her and she starts to question the morality of her gift. Even a character with a more "phyiscal" ability needs to be able focus so they can control their ability so they don't put other characters at risk.

I do agree that the characters that use the "power of friendship" as a magical trump card is kind of dumb. Unless the character finds the drive to give one more push to defend their friends and wins (think Digimon) - I can do without it.

LOVE THEM! A huge part of my own comic is actually about this and I think it's great when emotions are linked to powers, even just a little bit! It makes the emotionally intense scenes (which are the BEST SCENES) that much better in stories!

I've definitely dabbled in "strong emotions make characters stronger," where the adrenaline of the moment causes the character to push themselves harder than they normally would, sometimes even discovering powers they didn't know they had. That kind of thing is fun and can make for an impactful moment, but you have to be careful not to make their newfound power TOO absurd, else it can come off as too convenient.

Powers that rely specifically on emotions, on the other hand, tend to come with some pretty heavy drawbacks. A pretty famous example is the Hulk, where Bruce Banner turns into the Hulk when he becomes angry—whether he wants to or not. Another one that comes to mind is Steven Universe, specifically the episode "Steven Floats," where Steven discovers that he can float when he's happy... but how can you be happy when you're 20 feet in the air and are about to fall to your death?

I think that's part of why the whole "power of friendship" trope can be a bit grating, because it tends to manifest as a character suddenly gaining the power to defeat the enemy, with zero drawbacks, just because they thought about their friends and it made them determined! ...Pretty obvious deus ex machina when done poorly.

I'm generally a fan as it's a fun way to build some additional hype during a climactic moment. All good things in moderation, of course, but that concept has never particularly bothered me. Even a little Deus Ex Machina here and there is okay in my book as long as it's not over used (and even sometimes then, if I'm invested enough in a show I'll excuse it over and over- I'm just here to be entertained lol).

The main caveat that I don't like is when either only the main character has access to this emotional power up, or if it's very disproportionately distributed towards them (maybe another character is able to do it once during a pivotal moment in their character arc but never again, or something while the MC does it all the time). This mostly only applies to ensemble casts and longer series that aren't focused on telling a tight story about a single character. If everyone else on the cast has to "play by the rules" but the MC can just ass-pull emotion boosts whenever it's... meh to me.

It's not exactly emotion-based, but it reminds me in the digimon animes, for example. Only the main character and rival character (or sometimes just the MC) can attain the highest level of evolution- everyone else gets stuck 1 or 2 notches behind as their character arcs either resolve too early or they just "don't find the same bond with their digimon as those two". So then in the latter part of the series every main conflict is obviously resolved by the strongest character(s) while everyone else is left to either stand to the side or deal with minor threats otherwise. Stuff like that irks me regardless of what the source of the power boost is lol (not always enough to stop watching, but it's sad to see some of your fave characters get shoved to the side ;u; )

I actually love it so much that my entire magic system is this.
Every character in my story has a power that is deeply tied to who they are as person, it fits their core personality and is perfectly tailored for who they are and how they act... Even if they might not like it themselves.
YOu can often understand a lot about a character from the powers they wield in jTA.
But the kicker is... The bad sides of their personality also affect how the powers work, like, a person who is coodependent has powers that don't work well without another person, and a person who can't make up their minds has an unpridicatble element in their power... And our protagonists, welll, they have a fair share of issues with each of their powers.

Here is the thing, i actually don't like the 'rage state', it is inevitable in my scenario where magic is bound to feeling and personality, so when it does happen it is usually because the specific person has a serious mental condition that if left unadressed would consume them both physically (via their magic) but also mentally (by the problem itself).
I don't enjoy watching characters rely on their 'rage state' to fix things in shows, instead, I want them to feel like it is a problem that needs to be solved to not endager their lives and the lives of other, rather than a tool that they need to learn to control... and one of my characters has an arc that is a commentary on precisely that trope ^^

Neither
There is no concept, only execution

It becomes shallow when overused, as you stated, but for the most part I think it works well with magically-based powers. I've built allowances for that kind of thing into my story, as the way the source of magic is linked to one's connection with themselves/the cosmos, so in moments of high emotion of course a mage would be able to draw on more magic. But the caveat is if you channel more magic than your body is equipped to handle, you can do significant damage to yourself; potentially even die. I think that helps balance things out a little!

There's also some correlation to physical strength and emotion in real life! There are so many stories of, for instance, mothers lifting cars to free a trapped child. (Often damaging their own bodies in the process.) Feats of unusual physical strength in life-or-death situations are pretty well documented. It's like some limiter in the human brain, moderating our strength so we don't shred our muscles to bits, gets switched off in those moments. Fascinating stuff.

Hate them.

"My emotions are stronger than yours" it's tired, overused and very little thought behind it in many cases.

If I remember something from the first year of psych uni (I have a BA in psychology, didn't pursue further) is that people can feel high intense emotions for the most trivial things. That means with emotion linked powers, someone who's hamster died may be able to wipe the floor with someone with years of trauma because in the moment, hamster girl's feelings are all over the place and at a high intensity.

Imagine it: A chaotic flare of energies, some high some low, never constant, barely any pattern, difficult to control and quite volatile versus a constant stable power coming from a single stabilized mix of emotions.

Everybody forgets the adaptability and acceptance of the human mind. Many, can live with the greatest pains. And in time, happiness, sadness gets dulled as the memory becomes ever more distant. You end up with a scar. Now that might bring forth neurosis, but in the context of powers, it would mean that your abilities decrease in power with time. You'll go from death ray to laser pointer.

Try to recall a point in your life when you were in an emergency situation, physical intense action like combat, action sports or any action packed activity. What did you feel? In my case, it's a mix of tension, heightened focus, and enhanced control over my body. What I know is that I don't have time or the ability to recall being sad, happy or in love.

I wouldn't be able to use any powers other than the ones derived from what I'm feeling in the moment, any deviation would also break my focus, body control and worst of all, distract me. Which in turn would make the only powers I can use, lose intensity. Laser pointer again.

The only way would be to keep out of the main conflict and constantly hurt yourself in ever increasing creative ways to keep it up. So you either break yourself mentally and end up in an asylum or become so desensitized that your abilities will barely compete with a regular weapon.

It felt good typing this. I get minor fireball for like 5 minutes.

hey, that's pretty legit, you changed my mind, kudos!