I just did the opposite at PHX last week from AA to SWA. It was a little pain having to get out of the airport, catch the bus and go through security again.

Assuming you are not checking bags, I would leave not less than 90 minutes connection time, but ideally 2 hours in case of a small delay.

There is certainly TSA pre for SWA gates, but I don't rememeber for AA gates. Regardless, my experience with security in AA PHX gates has been fine in the past (I think they only share that concourse with a handful of other airlines with hubs somewhere else).