The browning is a far better gun than the remington so you shouldnt have the same problems if everything is clean and functioning properly. I found 160 grains to be pretty good, as far as energy retention and a higher b.c. Their is no point thinking about 180 grains as 175 is on the top end for the 7 mag. I shoot a 160 partition in my 7mag and dont feel I need anymore than that. Without looking at my loading books i think the 175 grain actually has less downrange energy than the 160grain. Shoot them both and see what your gun likes!
If you put a post on this site and said that you needed to have a 180 grain bullet to shoot a moose then I would expect a ton of replies saying they have shot moose with 150 grains in a .270, or a .30-30, or lighter caliber guns.. I have several larger calibre guns but see no reason to use them for moose.. 7mm with a 160 is plenty! To say you need a 180 grain bullet or larger is very vague.. A 160 in a 7mm rem mag is more potent than a 180 in a 30-06, and certainly a .308.....