I think Jeff Bridges is great in Crazy Heart but that Mickey Rourke is even better in The Wrestler. It's tough to say why exactly but it doesn’t have to do with a "narrow, unchallenging role" I don't think. After all why is it more complex and challenging playing a battered professional wrestler trying to get back former glory than a self destructive battered, alcoholic country singer songwriter with real genius who has given up on any chance of former glory?
(Sidebar-- but when lately has there been a braver, more affecting performance by an actress than Marissa Tomei's in The Wrestler?)
I think it has to do with Rourke's sheer emotional resonance. In fact a case could be made for the more challenging and wider role to be Bridge's. His character has some things the Rourke character didn't have: self destructiveness, creative genius, acute intelligence, his song writing, and real artistic talent, his performing expertise. The way these things keep shining through even in his most drunken performances in the lowliest of dives--I've seen dozens of such wiped out, forceful, great talents in my lifetime of going to grungy blues clubs--is a marvel of great and subtle acting. So too is the understated and believable relationship between him and Colin Farrell, which steers so wide of clichés about Nashville ersatz country misappropriating real country.
Also I'm not sure that Duvall in Tender Mercies--my all time favourite "small movie"--is so superior to Bridges in Crazy Heart. I'd prefer to say they were both superb and different for all their similarities. Duvall was about gaining redemption; Bridges was about gaining equilibrium.
And in the same way I'm not so sure that Tender Mercies is so superior to Crazy Heart. But this I can say: even more than Tender Mercies, Crazy Heart--through Bridges himself, part of the greatness of his performance in fact--reminds us and illuminates the prosaic, heart breaking genius of the greatest country music.