I have a Zyliss as well, and it's good, except when you're trying to grate the hard rind on Parmesan.
If you have a food processor, with a grating/shredding attachment, you can easily grate/shred cheese with that. The trick, is the plunger. You need to drill a couple small holes in the corners, then load the plunger with a little cornstarch. As you grate the cheese, shake a little cornstarch in. This keeps the cheese from sticking to anything and everything. With parmesan, you might not need to do this, but for cheddar, co-jack, or any medium-hard cheese, it's a god-send.