USNA does not play D1 hockey. Both USAFA and Army do, and both play in the Atlantic Conference, which is among the lower regarded leagues in D1, but still quite competitive (there are only 60 schools which play D1 hockey, and anyone team can beat any other team on any given night).
My kid is at West Point, so I am biased, but even though Army finished higher in the regular season standings this year and hosted Air Force in the league playoffs, AF won the series, and ultimately made it to the NCAA tournament (for the second year in a row). AF followed that up by beating the #1 team in college hockey this year, St Cloud, before loosing to Minnesota Duluth (last year's NCAA runner-up) last night.
In short, I think AF has the better program between the two. Although the teams are very competitive.
As for the club teams, I think all three schools have club programs. I don't follow the club hockey like I do D1 hockey, so I can't comment much, but not having a varsity team probably gives navy a bit of an advantage with the club program. That likely varies from year to year though.