I'm fairly new to having my own sidecar, but do have experience as a monkey on an offroad MX type sidecar.
Its probably really not that important if aren't doing anything harder then rough dirtroads.
However, if you are going to buy a Ural anyway. Why not get one w/ the 2-wheel drive? In my opinion that would be the only reason to go for the Ural. (Though the "modern vintage" thing is kinda cool)
I've also never driven a 2wd rig, so take that for what its worth.