You're talking about the so-called "tone-plate", that does make a dif, the GoW Moneys have a bit more bite than a reg Doublecut.
I second what has been said. The Money/Doublecut looks and plays like a modern bass, but sounds in a world of its own, neither really vintage (too nuanced for that) nor modern, neo-blurry. I can see it doing well in a blues band, it will musically melt into the band sound and give it warmth, never overbearing, but always heard, without needing the high-end snap of a P. OTOH you'll never get that attack out of it you have with a P.
You really can't compare the two, the P can't do what the Money/Doublecut does and vice versa. For use in a blues band the Money/DC is the more original and setting apart choice. But someone who likes the snap of his P Bass might find the Gibson less immediate though it is far from sluggish.