Both are fine cartridges, you might also look as the 7mm S.T.W. but for moose you would want to hand load. These kritters are big, and tho not nearly as hard to kill as simular size African game, you want penitration. This means heavy bullets with good sectional density. In 7mm you want the 175 grain and in .30 I would go for the 180s. Pick a good bullet as all the power in the world does not make up for bullet failure. I would recomend Federal Premuim if you do not hadn load. Up here in Maine, at my shop Remington CorLoss has gained a bad reputation with my customers, if you can not get the Federal I would go with Winchester.
As for a cartridge for moose, I would go for the .366 D.G.W. , but of the two you mentioned I would select the .300 Winchester on the merrit of the heaver bullets. You will get more recoil and if this is a problem go with the 7 mag and 175 grain slugs and you will be fine.

Your Friend
Jud