No one in the Army that has ANYTHING to do with helicopters calls them "Choppers". The usage pretty much fell by the wayside a few decades back. Only people whose only experience with heicopters is watching MASH on TV call them "choppers."
We called them everything else though. Usually people used the propername (e.g. Apache, Cobra)or defacto nickname for the airframe itself. (like "Slug" or Huey for the UH-1) Often it's just an abreviation of the proper name, i.e. Hawk, Hook, Crane, "58", "64", etc.
Collectively they're simply called aircraft, or helicopters. Alot of times we'd refer to them as "airplanes" even though it wasn't technically correct.
Possesively we'd refer to them as "birds" or "ships". As in, "We'll take Aviator's Bird." or "This will be a two ship mission."
Unfortunately there isn't a slang term that's used in toto that will cover all Army aircraft, other than "aircraft."
Ross