My personal opinion on this sort of connundrum is this- the universe isn't fair. There will be someone who seems damn near perfect, and there are those who seem like their entire lives are one gigantic tragedy or sitcom moment after another. However, the reality is that the perfect people do have flaws, and the cursed do have their good moments. So, there's room to maneuver on this one. Many folks want to see the good guys kick butt without equal, especially those who want inspiration when the real world around them is sorely bereft of such heroes. Others want someone that can empathize with to rise up from mediocrity to become a hero, the Everyman Hero, so to speak. Both work well, in my opinion.
Another thing to bear in mind is that the flaws of superhuman or perfect characters need not be overt, but even when subtle it should be written in such a way that the reader can cognate it early on and not be put off. One of the main criticisms I have encountered from those who have read my works is that some of the races or characters seem superhuman. I have found that the critics missed the flaws they have because they were so subtle in the writing, and went back and fleshed them out a bit more. I agree that you want room for your character to grow, but it need not necessarily be in their niche of expertise. The male protagonist of the first three books in the series I am writing is an experienced and quite powerful warrior, and is of a race that excels at that art. However, he has never had much experience in serious relationships, and thus his growth over the book is emotional and social as he falls in love with the female protagonist. You can find a lot of examples of this in Jim's books, such as Butters. All in all, I think the approach you should take is entirely up to you, as every writer has different styles and every reader has different tastes.