Is zoom quality better with a small frame size?

[Paul Franklin Stregevsky]

Could a zoom lens designed for an APS-sized sensor have less distortion or
vignetting than a zoom lens designed for full-frame 35mm? In other words, is
it easier to design a "no compromise" 5:1 or 10:1 zoom for the smaller
format? Would a hood, for example, be able to work well over a greater range
of focal lengths?