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Microsoft changes Hyper-V in each version, which creates a learning curve for IT staff with every new Windows relase.
VMWare has more third-party support, bringing all kinds of options for backups, vm syncing, and vm migration that aren't available natively or from Hyper-V.
Well, VMWare has been around longer and is arguably more fully developed. It's number one for a reason - most of the bugs have had plenty of time to be worked out, people are familiar with it, and in my experience it is easier to find people that have experience with VMWare than Hyper-V. On the other hand, Hyper-V is easier to learn, and has the advantage (in some situations) of being a Microsoft product, so if you happen to operate in a Windows only environment, it can save you a lot of money by allowing you to run virtual machines without requiring you to pay for additional server licensing.
Here is a handy chart that breaks down the nuts and bolts of the two. You might find it helpful. http://www.techrepublic.com/photos/marys-shoebox2/280735?seq=102