Both products provide an interesting contrast in the things they focus on. For right now, Parallels is all about Windows. It supports Linux, but you lose Coherence (the 'rootless' feature, where your VM applications appear to coexist with your Mac OS X applications), and a number of other conveniences. VMware has more mature support for Linux on tap for Fusion, which is no surprise VMware has a more mature product line. However, Fusion is still clearly in beta. For example, I still cannot get the VMware tools for Linux to install in my Ubuntu VM.
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Even in its beta status, VMware Fusion for Mac OS X shows the advantages of having richer heritage. For example, even though it's not perfect, there is accelerated 3-D support in Fusion. This is important not just for the obvious use of game playing in a VM, but for running 3-D and other graphics - intensive applications that aren't on the Mac yet, like 3D Studio Max, Autocad, Expressions, Acrobat 3D and Designer, etc. Yes, that's right, 3D isn't just for games anymore.
Another benefit of VMware is the ability to assign CPUs to a VM. Now on a dual-core system, like my MacBook Pro, this isn't such a big deal. But on a Mac Pro, which is running four cores, this can come in rather handy, as you can now assign cores to VMs as needed. If you want to run multiple VMs, (and who doesn't), this feature doesn't suck.
Both implementations have a "Physical to Virtual" system, Transporter for Parallels, and VMware Converter for Vmware. Both do essentially the same thing, help you convert a physical machine to a VM. Both can also convert other VM's to their own native format.
One advantage here for Parallels is that it can convert VMware images, whereas VMware converter doesn't (as of yet) deal with Parallels images. Neither handle Linux or Unix directly. The advantage VMware has is in scale. You can use converter either locally on a Windows desktop, or you can go to VMware's Virtual Appliance Marketplace, and download preconfigured VMs. Need an appliance, (VM) preconfigured with Zimbra's messaging environment? Done. Need an Oracle 10g appliance? Done. That's part of what you get when you're the little brother to something like VMware ESX, VMware's enterprise offering.