Although the 375 H&H is enough for the moose it is a little light for the big bears
so I would go with the 375 RUM.
The 375 H&H with the 260gr accubond has 2000 ft/lbs of energy @ 475 yds.
The 375 RUM with the same bullet has 2000 ft/lbs of energy @ 675 yds.
The H&H produces 2000 ft/lbs of energy at 425 yds with the 300 gr bullet.
and the 375 RUM produces 2000 ft/lbs at 550 with the 300 gr bullet.
Drop with 260gr- H&H= 130" @ 675 yrds.
RUM=99" @ 675 yrds.
Drop with 300gr- H&H= 89" @550 yrds.
RUM= 72" @ 550 yrds.
If the shots are all going to be less than 100 yrds then it doesent matter except
when confronted by a large brown bear intent on ruining your day then an extra
1000 ft/lbs of energy @ 100 yrds could improve the odds.
Assuming a moose weighs 1500 lbs the H&H is recomended to 125 yrds the RUM
will have the same energy @ 275 yrds.
With that said you be the judge as to what you want to hunt with.
J E CUSTOM
I dunno .375 H&H has been used for dangerous game in Africa for over 100 years...