I tried an American Pro P on Saturday, and A/B'd it against a new G&L LB-100. The Fender was alder/rosewood, and the G&L ash/maple, and the strings on the Fender seemed slightly dull. Even accounting for these factors, I was surprised by the G&L's additional clarity and punch. I still liked the Fender though, and want to try one with a maple board and completely fresh strings. Playability was similar, which is no surprise now that G&L has adopted Fender specs with a 1.625" nut and 9.5" fretboard radius as standard.
To update, today I visited a GC, and found two LB-100's (ash/maple and alder/rosewood) and an American Professional P (alder/rosewood). All had fresh strings, so this was a more useful comparison than my previous one. I ran them through a G-K 700RB-II and Neo 410 rig. (I have a 700RB-II and Neo 112 cabs.)
Not surprisingly, the G&L's sounded almost identical to each other, despite the wood differences. The alder/rosewood may have sounded slightly thicker in the lows, but I'm not confident in this. They both sounded fantastic, exactly like I want a good P-bass to sound. Classic vibe, with lots of punch and a wonderful range of sounds just using the tone control.
This time, with more lively strings, the Fender sounded almost identical to the G&L's, but with slightly lower output. It had more punch and clarity than my 2004 Am. Series did with its stock pickup, and it's good to see Fender making progress there.
So, they're both great, but as usual I prefer the G&L. For one thing, due to a finger joint problem I play mostly with a pick, and the G&L bridge is
awesome for palm-muting with a pick. With Plek fret levelling, they also can set up with lower action, at least IME, but a good Fender (like my 2003 Jazz) can get very close.