Never found normal (25.4) size stuff wanting in the stiffness department myself, particularly if you use decent kit (Thomson, Easton, Raceface for example). That said, 31.8 is pretty much guaranteed it's not going to be weaker!
Put it this way, if you've got some 25.4 bars and stem lying about, then they'll be fine. If buying new, mainly because of the extra choice and the fact that not much good 25.4 stuff is made any more, I'd buy 31.8. I've gone 31.8 on my bikes now (well, all but one, but that might end up going 31.8 soon enough) mainly for intercompatibility of parts between the bikes, and also so I don't have to mess about with different brackets for my bike light.