You don't need to both filter and chemically treat water on the AT; overall I found the water there to be quite good, a lot of it coming from springs. Depending on where and when you might find tannins in the water, but that's just a "look" thing, and not a safety issue. The only times I had to get water from a non-flowing source (i.e., a lake) was once or twice in Maine.

If anything, the difficult issue for me was the temptation to not treat at all when getting water from springs. My hiking partner and I often did not; in New York I came down with giardia (or something like it), but for whatever reason he didn't. I have no idea whether I got it from a water source or in town or what, but I would treat the water in some fashion. The Giardia-like (I was never tested) cooties put me off trail for just over two (quite frustrating) weeks.