EDIT: Is it just me or do you die way fucking faster than in GTA IV? I'm trying to steal a fighter jet, but I die in mere seconds, the heaviest armor doesn't even help much.
I ended up parachuting into the hanger and stealing the jet. A head on attack never worked because the tanks always blew me up. So your best bet is to parachute into the hanger or fly a helicopter in there and steal it. It took me forever but that's how I finally managed it.