Intel's first quad core was Kentsfield in 2006. It supports VT-x. AMD's first quad core likewise supports AMD-V. The newer virtualization extensions mostly just improve performance a little or do things you probably won't use anyway like SR-IOV.
The thing that matters more than the CPU for idle power consumption is how efficient the system's power supply is under light loads. The variance between them is large and newer power supplies aren't all inherently better at it.
I remember back in the R710 days (circa 2008 and Nehalem/Westmere cpu's) that under like 30% cpu load, most of your power draw came from fans that you couldn't spin down below a certain threshold without an firmware/idrac script, as well as what you mentioned about those PSU's being optimized for high sustained loads and thus being inefficient at near idle and low usage.
IIRC System Idle power profile on those was only like 15% CPU (that's combined for both CPUs), with the rest being fans, ram and the various other vendor stuff (iDrac, PERC etc) and low-load PSU inefficiencies.
Newer hardware has gotten better, but servers are still generally engineered for above 50% sustained loads rather than under, and those fans still can easily pull a dozen plus watts even at very low usage each in those servers (of course, depends on exact model), so, point being, splitting hairs over a dozen watts or so between CPU's is a bit silly when your power floor from fans and PSU inefficiencies alone puts you at 80W+ draw anyway, not to mention the other components (NIC, Drives, Storage controller, OoB, RAM etc). Also, this is primarily relevant for surplus servers, but lot of people building systems at home for the usecase relevant to this discussion often turn to or are recommended these servers, so just wanted to add this food for thought.
Again, lots of variables there and it really depends on how heavily you intend to use/rely on that sandbox as to what's the better play. Regional pricing also comes into it.