Here are the steps I took to move the vCenter VM from one cluster to a new cluster with new storage. This new cluster also had hosts which were of a different CPU type.
1) Remove any snapshots from the vCenter VM.
2) Clone vCenter server to new cluster and/or storage.
3) Configure new vCenter clone with proper hardware, network, and switch settings.
4) Make note of which ESXi hosts each vCenter server resides on.
5) Power off source vCenter Server – I issued this command while still in the vSphere client and then disconnected from vCenter and connected to the ESXi host that vCenter resides on. I did this to monitor the shutdown. Monitoring the shutdown is optional.
6) Connect to ESXi host where the vCenter clone resides.
7) Power on vCenter clone.
8) Connect to console on new vCenter clone – Logon to the machine, you will most likely need to configure the network settings and/or reboot the machine once more after new hardware is detected (if the host machine is a different architecture).
9) Verify the new vCenter can connect with the vCenter DB and verify you can connect with either the vSphere client or vSphere Web client.
When the new vCenter clone was done configuring new hardware and such it was up and running without any issues. We left the old vCenter machine around for a few days before we removed it.