The second big difference between the two: Only Parallels includes accelerated 3D graphics in Linux virtual machines, so if you need that, you'll need to use Parallels.
Advantage: Parallels Desktop.
The third big difference: If you want to explore operating systems other than Windows, Fusion offers a much broader universe of alternatives. Both programs support "virtual appliances"—dowloadable, pre-configured operating systems, often bundled with specific applications. VMware's appliance library is huge, with over 1,900 appliances available; Parallels Desktop' library, on the other hand, contains only 98. (Desktop can use VMware's appliances, but they must first be converted to the Parallels format; it doesn't really seem fair to give the program full credit for that capabiity, if it's reliant on the VMware ecosystem.) So you want to explore the wild world of operating systems and applications, Fusion is the way to go.
So much for the three categories with relatively clear winners; now for the more subjective criteria.
Purchase and license
Fusion and Parallels Desktop both normally cost $80, but pricing for both is a moving target. For example, VMware is currently offering Fusion at a promotional price of $50. Meanwhile, Parallels will sell Desktop 7 as an upgrade to owners of older versions for $50; if you're currently using Fusion, Parallels will sell you Desktop 7 for $30. No matter how much you pay for a virtualization program, remember that you'll also need to factor in the price of Windows itself.
There's a big hidden cost in those prices: the software license. Fusion's license (for non-business users) allows you to install and use it on any Macs that you own or control. Parallels Desktop, on the other hand, requires one license per machine, and it uses activation to check those serial numbers. So if you want to run your virtualization program on more than one Mac, Fusion will cost less—potentially much less.
Advantage: Fusion (for the moment).
Installation and general operation