Is it strength or weakness that makes a character.

This has been on my mind for a long time, and first came about when I found I could never seem to 'get into' a Superman book because he gave me nothing I could relate to.  What actually sparked this blog however was a small thing I noticed now that i'm starting to pick up DC books. I was recommended some books, one of which was Identity Crisis which I picked up and found myself interested in the Green Arrow character.  I went to the shop the next day and picked up a few books which included Longbow Hunters and Year One.  Year One is solely a revamp of the Origin story of the Green Arrow, while Longbow Hunters is set in the later years of the character, but included some flashbacks and dialog about the origin of which I was unfamiliar until reading this story.  In Longbow Hunters the Green Arrow recounted his story saying effectively that others had embellished it and that he barely survived this encounter and much of what was said was over-grandiose.  In Year One he was a super bamf archer immediately after picking up a bow and  took out an army single-handedly with makeshift weapons, in Longbow Hunters he said it was just two marijuana farmers. Towards the end of Year One he stated that he wouldn't tell what really happened because he didn't want the glory essentially retconning the whole thing.  I found myself enjoying the Longbow Hunter origin better, because it made him more human, it was more raw and more rooted in the real world.  
I think I've always enjoyed the street level guys because they face more danger at every turn, while the top tiers and cosmics were just so powerful it would take one of their own or a god-like entity to pose any threat to their safety.  Also, the 'weaker' characters have generally been the stronger characters writing wise, they have deeper stories etc, and I think a large part of this is a writer can't fall back on Pew Pew Kaboom as much. 
So what do you people think? Is it the strength or weakness that makes a character enjoyable?