The trick is you have to actually tell Social Security that you are getting that VA disability. This isn't something they automatically know. Please tell your attorney that you have the VA disability as well. If you're handling your case yourself you need to tell everyone at Social Security that you talk to that you have full VA disability and send in your paperwork to Social Security!
What happens if you don't have full VA disability? You should still mention it. VA ratings often go up over time as your condition gets worse. Social Security doesn't do partial disability. But we do want to know what your disability is. It's difficult for Social Security to say that you don't have a back problem if you're getting 40% VA disability for it.
Does it work the other way? Do you get VA disability if you're getting Social Security disability? Not really. The VA disability rating has to be service connected. You might be found completely disabled by Social Security but it doesn't mean it's for the same conditions that the VA is looking into and it doesn't mean it's service connected. You should tell the VA that you're getting Social Security disability benefits though. The Veterans Administration has lots of programs for disabled vets and it's worth checking out what you might qualify for.
Some other benefits that you may not know about - Social Security is working with the Wounded Warrior project. If you have 100% service connected disability and you were wounded in combat - your case will be expedited so you should get your disability approved in a couple of months rather than a couple of years. Again, it makes sense to let Social Security know that you're a veteran.
Other things to remember: Social Security offsets payments from workers' compensation and other states' disability programs. But Social Security does not offset for Veteran's benefits. Your benefits will remain the same and you can get money from both programs.
Veteran's medical centers are helpful another way you may not have thought of - all of your medical records are in one place. If we are trying to prove your disability far in the past (which happens some times) the VA is about the only place that keeps records going back decades. It's also just nice not to have to chase down records from dozens of doctors.
Obamacare has allowed everyone to have far more insurance options so you don't need to use the VA medical system unless you want to. But it's worth keeping in touch with the VA if you think you may have a service connected disability or taking advantage of some of their other programs. Being a veteran can help in ways you never planned on.