yep, I'm quite familiar with the ATA. i think basically that there was a major rift in the 70's when TKD was beginning it's roots in the US. The Kukkiwan in Korea was/is the main headquarters for TKD, it's students who went on to teach in the US disagreed with each others politics and all that.
I went to plenty of competitions (sparring and forms) where ATA and WTF and USTF etc all played nicely together.
Main difference between WTF and ATA from my point of view is the ATA includes weapons training at all ranks and the dobak is a wraparound style. WTF uses the v-neck style.
Our WTF school used only the Taegeuk forms; 1-8, then the ilyeo, koryo, etc black belt forms. It was completly traditional; only white, unadorned uniforms were allowed, it was very militaristic in the training regimen, commands were given in Korean only for most of the lesson (except for the newbs), people getting yelled at, LOT'S of team punishment in the form of knuckle pushups, rank testing was very stressful and tough, etc.