I would would say that a 30-30, 35rem, or 44 mag would all be better with the right bullet and have similar recoil to the 243 plus come in compact rifles. 308, 708, and 260 are also better choices that can be loaded to the same recoil level as the 243.

Not your listed choices...

If he practices, a rifle that fits him will probably be more important than recoil, but an animal the size of a moose will require a sufficient level of power.

I say buy another rifle that fits him in a larger caliber having a recoil level he can handle and also enough range: 308 or 708 bolt, 35 or 44mag lever... A moose hunt would be a big deal to me and not a regular hunt; wouldn't want to mess it up.