10mm width (cropped) vs 17mm width (full frame)

So would a full frame senser camera with a 15mm lens produce less vignetting than 1.5 cropped frame sensor with a 10mm lens?
Ideally i'd have the 10-22mm canon lens on a Nikon D200 but think there may be a mounting problem there (?)
Only alternative (even taking into account of using a full frame sensor camera) is the sigma 10-20mm lens, there appears to be no 15mm wide zoom made by cannon to use on a full frame sensor camera.....
Ideally i'd have the 10-22mm canon lens on a Nikon D200 but think there may be a mounting problem there (?)
Only alternative (even taking into account of using a full frame sensor camera) is the sigma 10-20mm lens, there appears to be no 15mm wide zoom made by cannon to use on a full frame sensor camera.....