'More competitive' has no real meaning. Both communities are about equal in size and activity, but both games have really different playstyles, so you should know what you are getting into :
-Melee has an emphasis on offense due to numerous movement techniques, more than in any other game out there. Its combos consist in short guaranteed situational strings that you can link together given that you perform the correct guess. It is highly technical and thus it is advised to stay focused on one character, whereas in Brawl it is a viable strategy to compete with a main and a secondary character (this is tending to become false as players get better though). In fact it is so technical that it takes usually 4 years to get good at Melee, when it takes half that to get good at Brawl (exceptions happen of course). Offstage play is a legit thing in Melee, and it makes landing a killing move much less of a chore than in Brawl.
-Brawl has a better shield and you survive much longer, which makes it a much more defensive game. The hitstun is very low, which means that every single one of your moves is a reset (that said, most characters in the top tier have legitimate combos and that's one reason they are above the rest). Brawl is played in tournaments on much more numerous stages (6 for Melee, 11 for Brawl usually). Wifi is terrible, but it's there, so you aren't doomed to stay bad if you live far from any other competitive player.
As for Injustice, we can't really tell how it is going to grow. The positive thing is that unlike with smash games, the skill you'll earn in Injustice will translate into skill in other fighting games. So even if it turns out to be filled with infinites, stupid matchups and bad DLC decisions, dropping it won't be that bothersome.