It is difficult to define competitive in the way that we mean it. One way you could put it is that it takes more skill to defeat a quality opponent in Melee than in Brawl. Another point is that there's more to learn in Melee. There's more options, thus more to think about. It requires a quicker mind and defter fingers. All these things lend to being more competitive at a higher level. That's not to say that these things don't help in Brawl, but Melee's requirements are higher.
The point about Melee being more competitive at a higher level of play may explain why Brawl supporters (hate that term) believe that Brawl is just as competitive. If you haven't climbed the mountain of Melee, you simply haven't seen the infinite possibilities in Melee. If you're not tourney level at Melee, but you play both games, then both will likely seem equally competitive. Once you have the higher level of play point of view, you can understand the competitive shortcomings of Brawl.
I don't mean to be condescending, and I know some people who argue for Brawl do have a good 'view from above'... but the thing is most of them acknowledge that Brawl just isn't as competitive while still enjoying the game.
Personally, I didn't have to play Brawl for very long to see the problems in it. My complaints from the first week I owned it still stand, and I've followed the ATs that come out. Nothing is game breaking enough to raise the skill ceiling to a point where a higher level of play does not consist of (IMO) obnoxious, boring, slow, repetitive matches.
I'm just gonna stop here so I don't go on forever
Hope I communicated my point well.