The server and DNS configuration you need for a subdomain is identical to what you need for separate domain. Possibly slightly more to manage if you are using the "naked" domain because of the DNS issue with not supporting CNAME records on the naked domain.
If you already have a wildcard SSL certificate for the subdomain a separate domain might be more work because you need a new cert and you don't if you stick with a subdomain.
The most work is actually buying the domain.
Then again, this is government we are talking about so buying a $10 domain is probaly three weeks worth of paperwork.