When cross vCenter Server operations such as clone and migrate was first introduced in vSphere 6.0, it required that both the source and destination vCenter Server (includes ESXi hosts) to be running the same vSphere version. With the release of vSphere 6.5, this base requirement still holds true (e.g. vSphere 6.5 for both source and destination), especially when performing these operations using the vSphere Web Client where mixed-vSphere versions is not supported outside of a rolling upgrade.

Having said that, it is possible and supported to clone or migrate a VM across different versions of vSphere 6.x, for example a vSphere 6.5 and a vSphere 6.0 Update 3 environment. This can be accomplished by performing a xVC-vMotion or xVC-Clone operation using the vSphere API. For the the xVC-vMotion use case, I have extensively written about it here and here and with PowerCLI 6.5r1, the Move-VM cmdlet has even been updated based on my feedback to support this capability natively. Furthermore, you can even perform these operations across completely different vCenter Single Sign-On Domains, which enables a new level of mobility for your VMs and access to resources of independently deployed vCenter Server instances.

UPDATE (11/01/17) - The following VMware KB 2106952 has just been updated to reflect what is officially supported in terms of Cross vCenter Operations ( Clone / Migrate) across different versions of vSphere. The matrix in the KB reflects what has been tested by Engineering and one thing you may notice is that Cross vCenter vMotion/Clone from vSphere 6.x to vSphere 6.5 is only supported when running at least vSphere 6.0 Update 3. After speaking with the PM, the reason for this change is that pre-vSphere 6.0 Update 3, there were no pre-checks in the code to prevent Cross vCenter Operations for un-supported target hosts such as ESXi 5.5, which could lead to poor user experience as well as undefined failure scenarios. In addition, vSphere 6.0 Update 3 also includes additional enhancements to properly clean up failed provisioning operations which will make Cross vCenter Operations much more robust. Due to these reasons, though it is possible to perform Cross vCenter vMotion from earlier versions, it will not be officially supported. I have also updated my summarized table below to reflect what is in the VMware KB, but please use the KB as your official source of truth for what VMware supports.

To help make sense of the different combinations of vMotions and cloning operations, below are a few tables to help outline what is possible and supported today.

vMotion

Cold Migrate

Clone

Virtual Networking Migration

Note1: vMotioning and/or cloning of VMs which uses the new vSphere Encryption feature introduced in vSphere 6.5 is not supported.

Note2: "Compute" only xVC-vMotion insufficient space issue has now been resolved with vSphere 6.0 Update 3, see this post here for more details.