Depending on heat treat, 440C should be a little tougher than VG-10 (once again, it all depends on heat treat). On the other hand the S-1 is a little thicker, I'd take the extra thickness of the S-1 if toughness is a major concern.
VG-10 will hold a better edge, and the Fallkniven is probably ground thinner at the edge (making it a better cutter). You can always re-bevel the edge though, and depending on your uses the Rant would probably make just as good a camp knife for 90% of what you'd use a knife for. Personally I'd be less afraid to do stuff with the Rant as well, given that it is so easily replaced if something does go wrong.
Knife to pass down to your kids = Fallkniven S-1 (though a Barkie would serve this purpose even better)
Knife to use hard at the campground and not worry about damaging it = BM Rant.