I've been out of the army since summer 2014. If I joined up with a different branch, would I go through BCT again?

Well I can tell you the Marine corps absolutely and the army since its been over 3 years if you were totally off contract yes. The air force and navy I'm not sure, But being prior service unless its reserve/air guard you would have a difficult time getting Active duty in those branches.

Check with a recruiter but seems to me that there was a 3 year window between exit and re-enlistment where you did not have to, if in the same branch. Pretty sure you have to go back through basic now as you have been out almost 5 full years. Again check with a recruiter as they would know and be able to tell you more definitively.

Years ago I joined the Navy after a being out of the Marines for 4 years. For them it all depends on the contract you sign with the Recruiter. As I said this was in 1984 so may have changed since.