I've never shot a moose with a 165 grain, and do know the X bullets usually act if they are a little heavier, due to their construction, But...
Moose are very big animals. Shooting a 30 cal, whether it be a 30-06 or 300, I'd go for the 180's or heavier. You really need a couple of feet of penetration on a big moose and you need a bullet that will reach the vitals even at odd angles and through heavy bone. The 300 is more than enough cartridge, but personally, I would increase the weight to 180, 190 or 200 grains. Nosler, Barnes, Swift, FailSafe, Trophy Bonded, etc... are all quality bullets and I'm sure you will find one that shoots well in your rifle.
Just my opinion...
YJ