The VA will only pay for or subsidize Veteran's who need nursing care due to a service-connected disability or any vet with a combined service-connected disability rating of 70% or more and who need skilled nursing care. The VA only provides nursing home care for individuals in other categories if beds and resources are available. This sadly does not happen often.
With Medicaid, it may be possible to live in a nursing community closer to home. This may be more desirable for the Veteran and his/her family. Another thing to consider is that in a VA home, the majority of the residents are men. On the flip side, most of the residents of a nursing home community are primarily women.