Yes, you are entitled to collect both veteran disability benefits and Social Security Disability benefits at the same time.  I advise my clients to apply for both at the same time.  A lot of times veterans will wait to apply for Social Security Disability until after they have been approved for disability through the VA.  This is a mistake for those who have not worked in several years because Social Security will not pay you past benefits all the way back to your date of disability if the date was greater than 12 months prior to your application date.