I've heard stories that it may make the body itself less rigid, so it's at risk of warping. And therefore some would say it's desirable to keep as much of the wood as possible.
I suspect that's a load of hogwash, to be honest. And even if it's not, I doubt it has any significant effect on tone - it may affect the acoustic tone a little, but I can't believe wood surrounding, or not surrounding, the pickups makes any difference.
But to hedge my bets, I'd personally go for the HSH route, rather than the full "swimming pool".