EF-S 10-22 appears to be a capable lens and I have heard no major gripes from owners. If the goal is an inevitable move to FF then the main question here is: do you invest in any new glass, especially relatively expensive ones, that will only work on the cropped sensor?
EF-s lenses may well go the way FD lenses went as FF sensors become more common and with more MP (in time). I know some continue to use them (FD), hell I have my A1 still

. Not an immediate danger for sure in the Canon line, but I don’t’ want to set off a war on the ultimate future of cropped sensors here.
I would always recommend that one invests in lenses that will have longevity and scope
beyond one's current body.
As I see it, the cropped sensor owner has advantages on the telephoto side with more reach for same Focal length and unfortunately a blunted wide angle limit... which is what you face. Most wide you can find in a rectilinear lens may be in the range of ~14mm which gives you about 22mm for the cropped body. about 4mm over the 16mm on 16-35II in the FF.
That said, most my cropped body friends with kit lenses are taken aback by how strikingly wide 24mm really is on a FF. The widest some have ever seen is 18mm with the kit lens which is about ~29mm in FF terms. Hence my earlier suggestion that a cheaper 14mm or an actual Canon 14mm (if budget allows) may tide you over till you hit the FF purchase, give you a modicum of wide angle thrills, and still allow you to keep the glass moving forward.
If you cannot live without the last 4mm to hit that 16mm on FF, then I am afraid you have to buy something like 10-22 EF-S.
That brings us to the age old question:
“Do you want it now? Or do you want it good!†