I've never worked at a Vet Center, so my take is based entirely on second-hand information, such as what patients and other VA staff said, as well as what I was occasionally able to see in Vet Center notes (which at least when I was in VA, weren't shared with VA). The eligibility criteria for care are a more stringent than VA, I believe, but it's also opened up a bit (e.g., I think it used only, or almost only, be for those with combat deployments). There were a lot more counselling center-esque treatments, like marriage therapy and readjustment services, that VA didn't always have available. Conversely, there was essentially no assessment. Patients also sometimes preferred going to Vet Centers if they didn't want to deal with coming into a VA for whatever reason. It seemed to me that the general acuity and complexity of the typical patient was lower than with VA MH, but that could vary by location. The quality of care provided seemed to vary widely, although there certainly sounded to be competent practitioners. They might have to deal with less overall SC-related frustration given the separation between Vet Centers and VBA/VHA. No clue how the compensation stacks up.
Again, I can't speak to the actual accuracy of the above information, or if any of it has changed over the past few years.