Hi,
Welcome to the communities 
1.My question is, can I just update the vCenter to 5.1, use the enhanced vMotion to move the VMs from one ESX to another or do I need to have the 5.1 version on the Hypersivor as well for enhanced vMotion to work?
If you are referring to EVC it will work for sure.But if you are in need of migrating the Vm without a shared storage both the host/vc should be in 5.1
You can also refer >http://www.vmware.com/files/pdf/techpaper/VMware-vSphere51-vMotion-Perf.pdf