Except during the TPAC departure bank in the morning. Lines can be ridiculous at the G checkpoint during this time.
I prefer the checkpoint that's wedged between G and T3 a few steps away from the Premier check-in desk. That or the checkpoint to Concourse E, which is now closed for renovation, is a quick breeze through security.
Expect to factor in at least 1 hour to go between Terminal 1 and 3 because you'll need to reclear security. There used to be an airside shuttle bus you could take between the two terminals to facilitate *A connections. It ran once every 30 minutes or something like that, but I don't know if this service is still being offered.