I'm pretty sure it's legal to carry 2 in IL.
The only time I could see it being usefull is when there is the chance to shoot both ducksand geeseat almost the same time. We always talk about having one gun loaded with heavy goose loads and one with lighter duck loads, but have never doneit.
Now if you're talking about 2 guns loaded the same, that's pretty much pointless, IMO. If you can't kill'em in the first 3 shots, you sure aren't going to kill'em by the time you switch guns and fire three more times at a birds a$$ while it's bustin' balls outta there.
'course, if you're talkin about snows, forget I said anything at all, i've never hunted snows