To add to snapfriend's answer, provided that both clusters are the same family of processor (Intel or AMD), what I would recommend is trying to set EVC mode on the old cluster and find the highest EVC mode you can set that supports your current processors. If there are no compatibility issues with your hosts, you may be able to enable EVC mode on the existing cluster without requiring the VMs to be powered down as long as the EVC mode you select directly matches the processors in that cluster.
If you can make that work, just enable the same EVC mode on the new cluster. At that point, you may be able to successfully vMotion the VMs to the new cluster.
As with most things, your mileage may vary, but I have successfully done this exact migration before, with the above noted caveats.