I have one of the new Paul's bridges on my WL McCarty, like Wedge. I can report what I'm hearing that's different from my earlier stoptail McCartys, with the caveat that the neck on my new one is maple, and the others were mahogany and rosewood, which is in itself pretty significant.
I'll confine myself to a few details I'm hearing in this guitar.
First, I'm finding the sustain of a note to be maybe a little more even up and down the neck. Granted, maple is going to ring a little differently, but what really attracts my ear is the evenness. Maybe it's a combination of things, but the bridge is obviously not impeding the sustain.
Second, there's not what I have in the past called "plinkiness" unplugged or plugged into an amp. Notes seem to be very solidly ringing. The tone is very clear and there's good separation of the notes in a chord.
Again, there are probably lots of factors combining here, including the choice of woods, other hardware, and what-have-you, but this is the first one piece stoptail that I've felt holds its own against the 2 piece bridge in that regard (though it sounds different from the 2 piece).
But the more I live with the guitar, the more the impressions of evenness and solidity seem to be reinforced. What I can't say for sure is how much of a role the bridge plays in this.