One difference is that the VA is a complete system, with it's own hospitals and staff. Medicare is that half-way solution, a public insurance system which buys medical services for the members from the private sector.

As for the VA system's woes, I would say: yeah, it's definitely possible to build a system that doesn't work well. But that doesn't mean we shouldn't be trying.

Medicare isn't really a socialized healthcare system. Most of the providers aren't government employees, and some providers don't accept Medicare patients because the reimbursement rates are low. Many beneficiaries actually obtain their plans through private insurers with the Medicare Advantage program.