For volunteer summer work, definitely more flexible about school name and less competitive than biglaw.
For permanent employment, less flexible about school name, and some are more competitive than biglaw. If you don't have a national school name, they will want great grades, journal, moot court, and/or judicial clerkship.
SLIP (paid) summer work will probably fall somewhere in between those extremes.
Don't confuse permanent hire with summer work. Summer work does not often lead to permanent hire like it does with firms. Sometimes SLIPs will be asked to return, but usually volunteers will not. Of course, this might depend on division/agency. However, across the board permanent hire will be much more difficult to get than summer work. USAO in DC, for example, has up to 100 interns every summer.
(My basis for the above is just based on my experience with one office).