At the beginning of Anna Karenina, Tolstoy famously remarked that "Happy families are all alike; every unhappy family is unhappy in its own way." I think that is one of the most profound statements about human nature that I've ever read. But we're not here to talk about human nature; we're here to talk about role playing games. Luckily, Tolstoy also indirectly summed up, with this pithy statement, how I feel about my player characters. Powerful characters are all alike; every crappy character is crappy in his own way.
And that is why I like crappy (i.e. Intelligence of 3, 1 Hit Point at first level, or whatever) characters. They're just more flavourful that way.