I think curved is a good choice if you are doing a lot of big-band section playing, especially live. The mics for the sax section will point down toward the bells of the other horns, and are generally at or above the players' head level, to accommodate flute pickup. Straight soprano will be "lost" in this situation, even more so if the band uses those "dance band" type stands.
Other than that, no difference (rather, the difference comes from the various qualities of the horn). I have owned all three types, and currently own a Martin straight and Venus tipped-bell. Both are great horns, in their own right. I used to own a Buescher curved, also a great horn, but alas it was stolen.
One factor that does, I think, make a difference, is whether the neck can be removed or not. I think the non-removable necks are a little more likely to play better, in general. (This means that some removable neck horns are just fine, and some fixed neck horns suck...)