Melee is much better from a competitive standpoint, due to features in Brawl which are unpredictable and break the delicate balance that fighting game aficionados always strive for in their games. For example, tripping, which is unpredictable. Then again, SSB has always been more of a "party fighting game" than a traditional fighting game altogether... There exist several mods that tweak the mechanics of Brawl so it plays closer to Melee for this same reason.
If you're not particularly into fighting games, though, Brawl might be the better choice for you, due to the bigger roster, the number of stages, the Story Mode (even if it's quite lacking), and whatnot.