I don't know abut prices, but the 16-35f4 is definitely sharper than the 2.8II across the frame. Of course the 2.8 was favored by indoor event photographers for the 2.8 which you can use to get a shallow DOF for close shots of table dressings and the like.
I haven't used the 2.8II, but I suspect it will be quite good at f8 compared to the 10-22, and decent enough away from the corners at larger apertures, which while certainly decent and good enough for most, is closer to the 17-40 f4 in IQ (but better in the corners at smaller apertures.
So depends a bit on what you want to shoot and how picky you are, but for an all-around UWA, I think you would like the 2.8II. It's going to be a lot bigger and heavier than the 10-22 though.