Monte Carlo: Has the best pool among the three. Gambling wise, most likely also has lower table minimum than Paris or PH.
It's been awhile, but room was very bland when I stayed there awhile back.
It does have a tram that connects to other MGM props nearby, such as Excalibur, etc.
As for buffet, probably the worst among the three hotels. Although it does have a food court as well.

PH: Not sure if it is considered a party hotel more so than some others. They do play loud music on the floor. The rooms here are better, and there is the Miracle Mile shopping there. Since Miracle Mile Shop is there, there are a lot of food options here.
Pool is probably the least attractive compared to the other two hotels. Free parking, although it could be a long walk from parking garage to lobby and hotel rooms.

Paris-Probably more "sedated" compared to the other two. Pool is nicer than PH's, but Monte Carlo may be better.
Buffet is much better than Monte Carlo's by a wide margin. Location is considered center strip whereas MC is considered south strip. Free parking garage shared with Bally's.

Hope some of this helps.