I personally prefer the double elimination. I don't like the triple elimination for the single fact that if your team is undefeated going into the championship game and loses, that's it, your team finishes second place. This happened to a team at the NSA states in Boardman last year. The team that won states had lost one or two games, don't remember which, and beat the undefeated team to come in first place.
Triple elimination is like a delayed single elimination, you're only guaranteed three games, after that one loss can put you out depending on where your team is in the bracket. I'm not sure why ASA is going to triple elimination, what was wrong with double elimination?