I think this question is more complex than would initially appear. What types of stories can you write with local (street-level) characters?
If written well, we can really see what drives a person, his motivations, his aspirations, his fears, etc. etc. all while being a relatively "normal" man (Batman, Captain America).
In the Spider-Man 2 movie, we see the scene of the girl offering peter parker cake. That scene is particularly poignant because that is one instance where peter is having a normal life...his rent his overdue, and his landlord's daughter has a crush on him. In other words to make these characters interesting, you have to be able to relate to them in someway, so their powers/abilities don't completely alienate you.
Cosmic characters are on the other end. For me, there's more of a mythology attached to them. Something abstract and mystical. For this reason one of my favorite characters is Galactus because the character was, when he was first introduced, supposed to be a comic book version of God. he's lost that lustre now but the appeal of cosmic characters for me is that they are fantastical while at the same time unexplainable.
They stop being interesting when someone ordinary is granted the power to destroy dimensions.
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"It is unwise to battle the Power Cosmic." - Silver Surfer
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Do you really have to ask who I want? global is pretty much my limit. "I am as far from a mutant as they are from you. I am, an External." Try and guess who said that.
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Interesting that so far, Global is least popular. Though my preference for established superhero characters is Cosmic (big surprise, I know), I find that in creating my own characters / writing stories, I prefer Global level: not so powerful as to be hard to relate to, yet powerful enough to be somewhat impressive.
Those who've responded so far, thanks for your input.
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i tend toward more local types, even if the character has a greater "threat potential" and they're simply operating within a smaller context. those types of stories seem to, as stated above, give a greater insight into the facets of the character. "street-level" types are the most relatable and interesting to me, as they're superhumans operating within typical human scenarios. or, alternately, they're relatively human operating in superhuman scenarios. it depends on the setting and other characters involved, at times.
comes down to the writing, mostly. but i can't seem to get too into the overpowered cosmic types. closest i can get is super-skrull.