I'm going to weigh in and say I think the bridge is an extremely weighty factor in the tone.
I'm comparing two JS-IIs, both bodies and builds obviously the same, one a '70, the other a '72 -
Both with Tonestylers in the tone control, the first position of which is a bypass so you get the full tone of the pickup. If I had decent recording equipment I'd post clips, but that may be for later.
In any event, one's got a Bisonic, the other a Darkstar. (There are other pickups but I usually solo the neck.) There's no 'suck' circuit on the '72 anymore, so I don't think it's a factor.
So, very similar pickups, but one's got the stock bridge with rosewood saddles, and the the other has a chromed brass bridge (maybe the stock bridge plate is brass too, I'm unsure), but also brass saddles, and instead of the thin plate screwed into the body that the stock bass has, it's got a 7mm brass plate routed and bolted into the body.
The sustain on the mod bridge is much greater, and the attack is brighter (both are strung with DR Sunbeams which are maybe 6 weeks apart in age), and the harmonic cross talk is more clearly defined, but richer in overtones. The stock bridge has greater fundamental presence, and less in the way of highs.
So it might not be "body" per se, but comparing the Guilds (I know the SFs and the JS series have the bridge in common) to other basses with set necks and mahogany bodies like comparable Epis or Gibsons, or even to B-series basses with the two-point bridge is very telling (though they're long-scale, so that might throw us).
In any case, there seem to be a few 'contact points' that are even more important, or rather at least as important, as pickups and body construction. (Though I guess a lot of people would just put 'bridge type' and 'neck type' into the whole 'body' category, but I prefer to be a bit more particular.)
