"With the first option above, if there was a suspected VXLAN issue, then it would be on the switches, multicast on switches etc? As there is nothing on ESXi related to config of VXLAN apart from vDS and port groups with VLANs?"
Correct, the VXLAN issue would likely be on switches since all it's doing is packaging L2 into L3 to get it across a LAN. There is no special config you need to use on the vDS.
"If you went for the second option above with VXLAN within the DC, is there a way to do that with VXLAN only! or would you need NSX for this?"
I'm not a Cisco guy but I believe you can use Cisco VXLAN between hosts to more easily present the vlans to the hosts. So... yes?
The advantage to using NSX (which uses Geneve protocol these days) is that it can seemingly take the overlay into the hosts and provide cross-site overlay via NSX Federation. What I mean by into the hosts is, by example, you have two networks on the same host with separate VMs trying to talk to each other. Instead of going out of the host to the network's gateway, NSX will have a distributed router on the host that can route the traffic and keep it inside the host. This reduces some traffic on your switches and can help with very chatty applications.
