Having done both, I'm pretty exclusively an AMP guy.
My AAMP experiences were a lot of prep with texts/calls back and forth and once you're in the door, its about getting the tip and going to work. I've also felt let down by the quality of the talent. Yeah, I might save a little cost, but its pure action with no humanity. It's like the provider is working on an assembly line. Maybe I've just had bad luck, but I'm not a fan.
With AMPs, I can roll in if I've got a spare hour and take my chances with or without any recon. I have discretion to pull the pin on the experience if I get a bad vibe - cut my losses with the chance of getting at least a shower if I need it and an adequate rub. And yeah, the mystery/build-up/anticipation is definitely part of the fun.