The fed actually pays pretty well for most of their IT and engineering jobs. Have a look on usajobs.gov if you think otherwise. The problem is, they almost all require TS/SCI, which is neither cheap nor easy to get. Also, if you are "inside the beltway" near DC, the commutes to the suburbs can soak 2 to 3 hours each way even if you live near mass transit. Living in DC on budget is, uh, iffy. Don't get lost.
The contractors are a mixed bag. Even though the companies often gets paid more for the positions than they would otherwise cost overall, the employees frequently end up either underpaid or are on contract terms that are not renewed and lack benefits.