Both the AS and BS degrees would probably give you a CTI certificate. This would allow you to apply to CTI announcements when the FAA is hiring ATCs.
However, you do not need to go to CTI school to be hired. You need three years of progressive work experience or a four year college degree. Four years of college would lead to a bachelor's degree (BA or BS). Two years give you an associate degree.
If you end up applying for another job later in life, it will look better to have a bachelor's (BA or BS) degree. It's 2 years more education than an associate degree. In this job market, an associate degree is pretty useless (no offense to those who have it). Lots of people have graduate degrees right now, so they're one level above a bachelor's. A higher degree means higher pay and rank in the real world.
I would also recommend getting a degree that is not in air traffic, so that you have something to fall back on if you don't get the job or if you are looking for a different job later in life. Variety will keep more doors open for you. The FAA does not care what your degree is in. My PEPC interviewer and I both happen to be scientists by education. Also, the FAA hires engineers and computer types, so if you want to work for the FAA in a different field a major in that could be a way in the door.
Then apply to an off the street general announcement once you have either three years of progressive work experience or a four year college degree.