I have an American Special honeyburst P, a Nate Mendel sig P, and I just purchased a MM Stingray 4H a couple of weeks ago.
The American Special is strung with Chromes flats and has that classic thump. It's neck profile is also my favorite of the 3, and the bass is nice and lightweight. The slim C profile is awesome, imo. It's the bass I'm most comfortable just picking up and playing, or working on new ideas.
The NM sig is strung with Roto stainless roundwound strings, and gets a great clanky, grindy tone when pushed hard. I lightly sanded the finish on the neck to get rid of the "sticky feeling" nitro finish. It's the heaviest of the 3 basses but balances nicely, and the neck profile is a little chunkier than my other basses, but still comfy.
The Stingray has the nicest feeling neck finish of all 3 basses, and the profile is between my 2 P's. It's a great feel, familiar yet different. I've currently got it strung with DR Sunbeams rounds. It's an aggressive, growly bass, and it responds very well to different right hand techniques and placement. The eq is also extremely responsive. It has the best slap tone by far (to me), if that matters to you. Some people also put flatwounds on their 'Rays to calm down the growl. The SR also had the nicest fret ends of all 3.
All 3 basses have classic looks and readily identifiable tones, and with proper eq'ing should be able to cover almost any musical situation. Go with the one that feels and "speaks" best to you, and you'll make it work, and be more inclined to play. I also agree with some of the other posters who suggest not limiting yourself to 1 bass. Hope this helps you.