Here are my thoughts on some of the key differences between Melee and PM that are important to me:
Aesthetics- Brawl and thus PM have revamped sound and graphics, but I really don't like them. Maybe it's because I grew up on Melee, I don't really know, but I much prefer the look and sound of Melee.
Character Balancing- This is one of the the only parts that I kinda like. I like to be able to play Kirby and Bowser and feel like I am playing a usable character. However, I will say that I am someone who occasionally likes to play bad characters because I think it's fun, and I feel like this is somewhat lacking from PM.
More characters- I don't like this at all. I'm fine with the amount of viable characters in Melee, and to be honest just buffing the worse characters is even pushing it for me. Having almost 50 characters (I actually don't know how many are in PM lol I could be totally wrong about this number) is way too much for me.
More stages- I like this about PM too. I think if Melee had eight or so legal stages instead of six then it would be perfect (especially when it comes to counter picking characters like Fox who don't really have a bad stage other than FD in certain matchups), but it doesn't so the PM variety is nice.
Slight engine changes- The games feel extremely similar, but since I am a Melee player of course I am going to be more comfortable playing Melee.
The competitive scene- The Melee scene is and probably will always be much larger than the PM scene, and I like the larger community.
What ThePuffDaddy said a couple posts above regarding being intentionally designed for competitive play and whatnot as well.
So these are all just personal opinions but I wanted to write them down. In the end I much prefer Melee over PM, but I think PM is fun sometimes too.