Very different products
Codeweavers has provided crossover for Linux for a number of years; it started as a commercial release of the WINE emulator on the linux platform. Unlike parallels, which virtualizes the CPU (making your client os think it is the only thing running on the machine), WINE works by intercepting windows API calls on the fly and translating them to similar calls on the host OS. There's a good deal of black magic going on there - API calls can vary wildly between platforms.
Crossover is a product with a limited scope: it allows you to run a few tested windows applications on non-windows platforms with a pretty good success rate. I've got a few customers who use it on Linux just to run Visio. Take a look at their supported applications here:
http://www.codeweavers.com/products/cxmac/supported_apps/ if the application you need is on the list, then it will work, and will work pretty well. It may not look *exactly* like it does on Windows, but it'll be close. If an app is not on the list, you're out of luck; it may work, it may crash. Your mileage may vary <g>.
Based on the stability of the Linux version, I have no doubt that they will eventually get there with the Mac product.
Parallels is an entirely different product with a very different scope - you aren't emulating a few instructions, you are running a whole new virtual machine. You can run virtually any software in the virtual machine that will run on the host OS - because as far as the app is concerned, it *is* running on that host OS. This opens a huge range of possible applications, and at a price that is radically lower than the current market leader (VMWare).
If you're only using Parallels to run MS Office, then Crossover may be a viable alternative, but you're getting a *lot* less functionality for your money. My money's on Parallels.
== Steve