Liquid for 98% of applications. If you get some serious cold weather, it can freeze. For true winter camping, you'd want the tablets. I doubt that would be the case on an AT thru-hike.
Be sure to tighten the caps. I had a buddy's bottle lead out on him on a 220M hike. The last 5 days of the hike he had to drink untreated water in the Sierras. Fortunately, he didn't get sick (he didn't just pick any water source; he was 'picky').