Both will work just fine for moose, as long as you place your shot accurately in the vitals.
That being said, other factors come into play, some of which have already been stated above.
Which rifle are you more comfortable/confident with?
Which is more accurate with the ammo you have chosen?
What is your limit for accurately placing bullets on target from field positions? Stay within it!
What environment are you hunting? Thick, dark timber or open prairies/fields/meadows?
How long is your average shot going to be? Short shot? Long shot?
These should assist in determining what retained energy you will have at the target. Deer = min. 1000 ft.lbs., and moose 1500 ft.lbs.
Bullet construction can be important on quartering shots where heavier bone is/may be encountered (monmetal or bonded) ...but many moose and deer have been successfully taken for decades with good old cup and core bullets.
A moose is a larger animal, but usually not that hard to kill...but like ay animal, each is an individual and some just have tougher constitutions and are more tenacious of life.
Deer, while smaller, can be more tenacious of life, so there are wily old whitetails that succumb to the 243, then there are the old warriors tat soak up some lead, and make it a ways before expiring.
In the end, which would work best under the worst shot presentation vs which will be best under perfect conditions...hope for the best and prepare for the worst...there is no such thing as being "too dead"!
I have taken many moose and deer with both the 300 (Win and WSM) and with 6.5's (Swede, and CM - still working on first with my 6.5PRC). They have both worked fine)
Have a great adventure!