Provided you match the field of view (by multiplying the focal length by 1.6) and keep the entrance pupil diameter the same (by multiplying the f-number by 1.6), then from a purely theoretical point of view, depth of field and the amount of background blur will be the same.

From a practical point of view there will be slight differences in the nature (including smoothness) of out-of-focus backgrounds between the two systems.

Assuming the 50mm lens on the crop sensor was designed for full frame (as almost all fifties will be), then there will be reduced occurrence of "cat eye bokeh" where out-of-focus highlights toward the edge of the frame take on an elliptical appearance due to clipping by the lens barrel.

The 80mm lens on the full-frame camera will probably be slightly smoother due to the more relaxed conditions of a longer focal length, specifically the edges to out-of-focus highlights should have a nice gentle roll off. To obtain good performance when wide open, most 50mm f/1.4s are over corrected for spherical aberration, which gives a harder edge to out-of-focus highlights which get brighter toward the edge, the opposite of what you want for smooth bokeh (for this reason the Canon 50mm f/1.2L was deliberately under-corrected for spherical aberration).

If the hypothetical 80mm lens has a wider aperture than f/2.2 then the out-of-focus highlights will take on a slightly non-circular shape (depending on the number and curvature of the aperture blades) in comparison to the 50 f/1.4, which if f/1.4 is wide open will have perfectly circular highlights as the aperture blades are fully retracted.