It depends on the level of your research. ANA is smaller, and devotes a lot of resources to young investigators, and is very "top heavy" meaning that a lot of the people attending the conference are movers and shakers. If you have an abstract and a research direction, you can get a lot of hands-on attention which can be great for your early career. The ANA is really for academic people and trainees.
The AAN is bigger -- but the date you mentioned is for the fall conference, which is not the annual meeting. The annual meeting of the Academy is in the spring. I don't know literally anyone who goes to the fall conference. Tons of people go to AAN (the real meeting, not the fall one), and many aren't very invested. The big cheeses are there, but the abstract sessions are a cattle call and you're more likely to get lost in the shuffle. The upside is that there is a lot of breadth (at the expense of depth). The AAN is how a lot of private practice people stay in touch with each other and catch some CMEs, maybe take a couple of courses. They've done some work in the last few years to really increase the level of scientific discourse, with decent results. MS tends to be huge there because it's a drug development darling and they pay for a lot of booths in the exhibit hall. And they have a fun run.