It is quite hard to say which one preferred by the most. I think Xen platform is widely used by many reputable service providers as it allows paravirtualization that offer complete isolation environment for each VM. On the other side OpenVZ which is light and mostly used by hosting companies that wish to offer the cheapest hosting packages.
Hello, I would have to say the most widely used platform for virtual servers would be OpenVZ mainly because it allows hosting providers to effectively and quickly deploy and manage virtual servers with capabilities of over committing resources. Though argued throughout the industry as a bad practice, effectively over committing resources properly will result in to negative impact for the customers and a larger profit margin for the providers, otherwise it would not be logical to offer such an option. However, Xen is the only platform that truly does not allow for the over commitment of resources, thus offering customers dedicated resources specifically for their environments. Some argue the same for KVM, however this is untrue, as RedHat prides themselves on the fact that like OpenVZ, KVM is capable of effectively over committing resources. The reason why you'll find that a Xen VPS will cost about 3 times that of the average VPS is just that, the resources that are allocated to you are dedicated.
In terms of flexibility openvz is better and when configured correctly it can be a beast, XEN is only good when configured correctly. A default settings openvz can perform better than an XEN that's not configured like how its supposed to be.