First of all, I'm going to say that I'm a casual player. As far as being competitive goes, I try really hard to beat my friends in our little party sessions and I watch matches online from time to time. I also kind of try to learn the advanced tech but that's just to look cool. :)
I prefer Project M to Brawl. I've not played Melee too much so I'm not aware of how different the speed is, or the physics, or even character balance. I like Project M for a few reasons.
1. Speed. Now, in my opinion, I like fast paced games. I do. I can totally respect your opinion if you don't particularly care for this change. It just feels so satisfying to move at those speeds.
2. Character balance. Before you raise your pitchforks, I'm just going to say that I don't know a lot about Melee or Brawl, balance wise, but I can definitely feel that there are characters in those games that aren't as rewarding to play as. Now, I'm not saying the balance in Project M is perfect, but I feel like the margin of difference in strength between the characters is a lot smaller. That means a lot more variety in matches and adds to the fact that every character feels rewarding, very fast. I also like the added and changed moves to characters like: the Pokemon characters being split, Ivysaur's solar beam mechanic, Zelda's new Din's Fire, etc.
3. Patches. The mod gets updated frequently so the meta can change, characters get changed, and sometimes new content gets added. Some people prefer having no changes made. I can understand this because you can get the hang of a character without worrying about them changing. I just prefer having changes so every character has a chance in the limelight.
4. Additional characters. I just prefer having a lot of characters because it definitely adds to the fun IMO. They already said that they won't add Smash 4 characters and I doubt that they'd add other characters outside of Smash (please correct me if I'm mistaken!). I therefore welcome the inclusion of the cut Melee characters. Roy and Mewtwo definitely feel better than ever.
5. Modding. I know this doesn't have to do with specifically Project M but changing the appearance of certain characters is so much fun. I recently added a huge pack of skins, stages, and music and bringing that to a group of friends turns that into a party.
6. Tripping. I never really had any problems while playing Brawl with tripping, but I'm totally fine with having a random feature like that removed.
I'm sure I'm missing a few things here and I'm probably wrong on a few things, but thank you anyways for taking the time to read this post!