I've seen 2 moose shot, both with 300 win, both hit well (through the shoulders) and both had to be shot again. That said...they were both probably dead from the first shot. However, a moose is the last thing you want to go chase through the "bush".

Personally I'd opt for the 300.

When I've been I've used a 308 Norma Mag which is real similar to the 300 win. Unfortunately I haven't shot a moose yet.