Safest to migrate all VMs to a host in the cluster, put host into maintenance mode, unregister the host from old-vCenter, re-register host on new-vCenter, join new cluster on new-vCenter (assuming Enterprise Plus license, then...) vMotion VMs from old-vCenter to new-vCenter. If you do not have enough hosts (like 1 extra host of capacity), you'll need to power off less-favored VMs to make room.
P.S. cross-vCenter vMotion is MUCH faster if the VM is left powered on (even if you stop most useful services) because when powered on vSphere uses the vMotion network (defined with MTU=9000 on fast switches). If the VM is powered off for cross-vCenter vMotion, then vSphere will select the Management network (likely only MTU=1500 on slower switches).