I personally believe P:M to be significantly better competitively than Melee. When I look at game balance and quality, I look at 1) how close to each other the characters are, power-wise 2) how varied the playstyles of the high-tier characters are and 3) how many characters are considered viable in tournaments.
So for my first point, Melee Fox is significantly better than every other character in the game. He isn't broken by any means, as many players have proven time and time again he is possible to beat, but he dominates the metagame to the extent that any character that doesn't do well against him doesn't stand a chance. Additionally, there is a very clear divide between the viable and non-viable characters, and characters that fall below that line quickly plummet in power and are essentially useless in tournaments (unless you're Gimpyfish). In Project M, Fox is still the #1 character in the game, but it's clear that the gap has been closed significantly. Additionally, I would argue that every character in the game falls between the power level of Melee Fox and Melee Ganondorf\Samus, so even characters considered "unviable" aren't totally useless.
For my second point, P:M wins hands-down. The Melee high tiers are very rushdown oriented, with the only exceptions being Peach, Ice Climbers, and Jigglypuff. Project M's high tiers, while still dominated by rushdown characters, now have far greater characters, with Mewtwo, Sonic, Snake, Diddy Kong, Pit, and several others bringing in greatly varied playstyles that, in my opinion, make P:M much more interesting to watch and play.
Lastly, as far as the number of characters considered viable, P:M once again wins hands-down. Melee's viable tier consists of Fox, Falco, Shiek, Marth, Jigglypuff, Peach, Captain Falcon, Ice Climbers, Dr. Mario, Ganondorf, and Samus, so 11 characters. Project M's definitely viable tier consists of Wario, Mario, Peach, Diddy Kong, Wolf, Fox, Falco, Shiek, Link, Mewtwo, Lucario, Ivysaur, Lucas, Pit, Meta Knight, Snake, and Sonic. That's 17 characters, and that's probably not all the competitively viable characters, just the ones that have proven themselves and are generally considered to be the best. Once the metagame settles down and people get better with some of the lesser-played characters, that number will probably go up.
To make Project M even more competitive, I think that the "lower tier" characters need to be carefully tweaked to become more competitive. The PMBR should also be cautious with the clone engine, because as more characters are added to the game it gets harder and harder to keep everything balanced. I'm sure the PMBR will keep doing a great job.