Usually ski crampons cannot be used instead of skins, but they complement each other. Ski crampons are good on steep snow with a crust or hard/packed/icy snow, where the edge of the ski doesn't cut through the surface enough. However, where crampons fail is soft snow, where the big surface of skins give much better traction. In short, ski crampons are most useful in ski-mountaineering when the snow conditions are less than optimal.

Supposedly the Europeans would much rather forget their skins than ski crampons at home, if that is any help. I tried mine without skins and it was pretty tricky.