I consider reverse P soloed to be more "modern" than traditional P. That's mainly because you get a bit more growl to the low strings, a bit more depth to the DG strings.
Of course it's all relative, right? Those who prefer traditional P might say that on reverse P, the low strings sound thin in comparison, and the DG strings less punchy.
As usual it's a matter of "different", with better/worse being personal preference. FWIW I lean toward the traditional tone of standard P, but I also have reverse P in my collection and enjoy that too. I mainly use reverse for modern rock & metal, but whatever, I'll use either config for any genre.
As for PJ -- what Roger said. Reverse P sounds more J-like on the DG strings, standard P sounds more J-like on the BEA strings.