Good training in any setting is valuable, especially if you’re able to talk about it in a way where you come off as competent. And as long as you have a license, you’re valuable.
IMO the biggest driver for hiring is supply and demand. For example, an org in a rural setting might want to recruit a psychologist with ample assessment experience but they’ll eventually settle for somebody who did an online LCSW because it’s better to have something than nothing.
A big benefit of AMC/VA settings is the opportunity to do multiple & varied rotations and receive specific supervision in speciality areas like anxiety disorders, PTSD, & eating disorders as well as medical setting ones like acute inpatient, rehab, etc that a typical outpatient only CMH might not offer on paper (or be capable of offering), which can increase your initial attractiveness to employers during your early career phase.
I always encourage people to pay a lot of attention to rotations offered and how the year is structured. And ask questions now before rank if you’re confused or want more info. You might find you’ll like some of these areas where you don’t have experience yet and pursue jobs as such in the future.
Once you’re further into your career, where you interned becomes largely meaningless as long as it was accredited since you will have accrued lots of experience and have other references.
And ultimately, how you feel about a place and whether it fits with things like location and cost of living is also very important for rank. Good luck!