Although it was straightforward to add the new host, I was unable to vMotion VMs between the two types of CPU as there was a CPU incompatability:
Okay, so the CPUs are different between the two servers, but they are both AMD, so I figured I could make it work by enabling Enhanced vMotion Compatability (EVC). Unfortunately, this complained that the CPUs were either missing features, or that the VMs were using these CPU features:
As it turned out, the problem was due to the virtual machines in the cluster.
In order to work around the error, I powered off each VM in the cluster, moved them to a host outside of the cluster, edited the settings of the VM, selected Options > CPUID Mask > Advanced > Reset all to Default.
This cleared a bunch of flags that have been set at one time (not by me; must have been an automatic change). Once that I was able to configure the cluster to use EVC for AMD "Generation 2" processors.
I was then able to cold migrate the VMs back to the new cluster and power them on. One problem though: How to move the vCenter Server and its SQL Server database VM into the cluster without powering it off. I tried to vMotion them while they were on, but got the same error as above.
The answer to this, courtesy of VMware knowledge base article 1013111, is to open a vSphere Client connection directly to the host running the vCenter and SQL Server VMs, power off the VMs, right-click on them and Remove from Inventory. Then open another vSphere Client connection directly to a host in the EVC-enabled cluster, and then browse the datastore containing these VMs. Once located, right-click the VMX file and add to inventory. This will register the VMs with the host and you can power them on (be sure to say you moved the VM when prompted). Once loaded (which can take some time on low end servers), open a new vSphere Client session to the vCenter Server and you should be able to see the VMs in the correct cluster.