Balance is a tricky thing to define. It depends on what your looking at. There are three main aspects to look at; top level (dominating characters), viable characters, and top/bottom character gaps.
Top Level:
Melee has 4 dominate characters. Brawl has as many as 3 or as low as 1, depending on how you look at it. Melee would look more balanced there, both in a percentage and quantitative basis.
Viability:
Melee has quite a few viable characters. Many would speculate that anyone in Mid or higher is, but for the sake of simplicity, lets say that only High and above are viable. That is 8 characters. Compared to Brawl, which has 16, Melee looses out.
Tier spreads:
In Melee, bottom tiers beating out high tiers isn't impossible, but its never done at important tournies. Select players defend the lower tiers, and their progress is noted and compared. On a tournament basis, lower tiered characters don't do very great.
In Brawl, the same holds true. Captain Falcons and Link's aren't taking the important tournaments. There is no glaring difference here between Melee and Brawl. Both games bottom tiers aren't capable of consistently taking tournaments.
In pools and such however, I find, from experience, that I'm far more concerned facing a low tier matchup in Melee then I am in Brawl, merely because gimping and comboing allow lower tier characters to take stocks off a few mistakes, where as in Brawl I need to screw up often allow enough damage to happen to take stocks.
Conclusions:
So, the question is, where does "balance" really matter?
On a competitive level, only the characters that dominate tend to win the "big" tournaments. They are the characters you prepare for, master the match-ups for, and practice against. Thus, to a competitive player, the only "balance" that matters is the balance in the top tier. Because Melee has 4 characters that regularly make it to Finals, the diversity to the tournament player is greater. Because the diversity is greater, the metagame doesn't stagnate. Thus, this is where "balance" in a fighter is the most important, and I would clearly say Melee is the greater game.
Viability comes in a close second, but viable characters are used far less, and their higher tiered counterparts often knock them out in the pools. Thus, to a lower end tournament player, who doesn't make it out of pools, or not very far in brackets, this is where "balance" matters the most. Brawl obviously wins here because the number of characters that can actually compete is larger.
As for tier spreads, both games stink on a tournament level. I never really consider the spread important in competitive fighting games, because the only thing that really matters is the highest end. Professional gamers aiming to take the wins won't use these characters, period. Clearly neither game excels in this category. However, I find Melee still wins in the end because the chances of actually overcoming a bad match up in Melee are far greater due to the severity of punishment in the game. In Melee, 4 mistakes can equal 4 stocks. That is never the case in Brawl.