I’ve been to both (several times) and I much prefer AAPW. Wrestle Circus was more polished and they brought in some established talent. But it always felt like a one-off event. There were no promos, no storylines, etc. You were just there to watch two people fake fight each other, with no narrative context. Kind of takes the fun out of it.
AAPW is rougher in terms of the actual wrestling. It’s a school, and the performers are students with varying amounts of experience and talent (some are really talented, though). But they put more effort into creating storylines and characters that make the show what it should be: a stupid soap opera that allows you to enjoy the obviously fake fighting as a work of immersive fiction. Hell, there was a turn at a recent show that even my wife was fucking stunned and upset by — jaw dropped to the floor, gasped, stared at the screen in shock — and she thinks wrestling is stupid nonsense (which… fair enough).
Plus, it’s like $20 and BYOB. Definitely worth checking out if you’re a fan of the territories from the 70s and 80s.