Often not, as Andy says. Because the same optical principles apply regardless of format.
But lens design includes a whole bunch of compromises, one of which is cost of course, but it's also true that if a lens only has to cover a smaller sensor area then that's one big limitation lifted.
For example, you can have more focal length range, or run lower f/numbers. Look at the incredible zooms we get on compacts, or the sub-f/1 lenses for M4/3rds, the f/2 zooms that Olympus makes. Can't do that on full-frame.
I think that if you were able to put a top grade lens from a M4/3rds camera on a full framer, or maybe one of the new Nikon lenses for the V1, then the performance would be astonishingly good, ie amazingly sharp. But you can't do that.
Bottom line is, when it all shakes out, bigger always wins.