Much slower SQL application performance after upgrading from Windows Server 2008 R2 to Windows Server 2012 R2
Originally self-answered in comments:

After doing a lot of testing, this issue appears to occur when crossing the temporary network bridge from our new environment over to our old environment. Although we haven't figured out the root cause at the network layer, we have decided to leave the centralized server on our old environment and move it last during our infrastructure migration.

We kept seeing a lot of ASYNC_NETWORK_IO wait types with the queries. After doing a lot of testing with different configurations and opening tickets with Cisco and vmWare, vmWare asked us to try to disable Receive Side Coalescing (RSC) on hosts.

After making that change, performance was back to normal (actually better on the new equipment, which is what we expected). See the VMware Knowledge Base entry:

After upgrading a virtual machine to hardware version 11, network dependent workloads experience performance degradation (2129176).