RE: Rem 7 mm mag or 7 mm mauser rifle?????
The 7x57 Mauser is a good step down in power from any of the 7mm mags. It' s a great cartridge and plenty for whitetail, but since you mentioned moose I' d go with the 7mm mag.
W.D. Bell killed quite a few elephants with the little 7x57, but he was shooting solids to the brain. I sometimes wonder how many he wounded along the way but didn' t write about.