Just remember 50mm is 50mm on crop or full frame. You might equate a 50mm on a crop sensor to 80mm FF, but the depth of fields are different for a similarly composed image since you have to move back on the crop camera.
A full frame image can be cropped at the center and it'll look the same as the crop camera using the same lens as far as depth of field.
No, the pictures will look different. The equivalent focal length on the crop sensor of 80mm still has the physical aperture diameter in front of it, so the effective aperture isn't as wide. When you figure full frame equivalence, multiply both the focal length and aperture by the crop factor, 1.6x for canons.
So, 50mm F/1.4 on full frame = 80mm F/2.2 on a crop camera in terms of what the image looks like. Depth of field won't be as shallow.