My experience with SSA has been easier. I was granted SSD based on evidence I provided from the VA. I was never formally evaluated by SSA shrink.
Be careful select as an attorney to represent your case. They usually aren't going to take your case until they see big dollar signs, e.g. you have been denied at least once or twice or you potentially have tons of backpay in which case the sychophants will take at least 1/3. Did you forward you VA results to SSA as evidenciary and in support of your SSD claim. If not I would serious consider this. Many SSA attorneys will at least give you a consult.
I think the key to being successful with any disability claim is to be thorough in gathering supportive documentation from; friends, relatives, providers (more than one), psycho-social precipitating events, write you own letter. Get someone to help you obtain the documentation and organize it. The VA documentation - if in your favor - might be better shared with SSA as well.
It's worked for some of my other brothers and sisters.