A research career at a VA does open up more streams of funding, especially as you move into early career. In general, I would steer you toward a Center of Excellence or Center of Innovation with a strong track record of transitioning fellows to full-time faculty positions. Hopefully the postdoc in question is connected to one of these resources.
Some of the decision may also come down to your research interests and who is available to mentor you. Some research interests will be a more natural fit with one type of environment than another. I also second AbnormalPsych's precaution about the red tape and general bureaucratic nonsense in the VA, but that doesn't always mean it's a lot better elsewhere.
I think the decision between two sites ultimately comes at least as much to local/site-specific factors as the more general question of VA-versus-AMC.