I own a Schecter Diamond P-4 and it is my main bass, I purchased it used from fellow TB'er Troy McClure. I considered others including Fender P's and the Schecter just felt right. IMO it does not sound "just" like a Fender P, it's actually quite different.
I also own a Squier P, which I rarely play and it is a backup to my backup (Schecter Raiden 4)
Personally I would recommend the Diamond P to anyone, as long as they understood that it is HEAVY, and weighted a little funny (slight neck dive, nothing crazy though). It is very versatile, too, with the coil tapped humbucker. One thing they do poorly on these is tone control. Basically, you're either "full tone" or "completely dumped" with no real in-between.
But overall I have been happy with my Diamond P and have no regrets. For the price, it's a great bass with very few drawbacks. If it were stolen I'd buy another one.
But you have to buy what you like. Nothing wrong with a Fender P. If there were, it wouldn't be so prominent with bassists.
Jerry A.K.A. "Thumper"
Schecter Bass Club Member #290
Owner Of A "Basswave" Carvin SB5000
Country Bassist Club #1
Mediocre Bassist Club Member #788
Carvin MB Combo Club Member #3