I agree with Stubblejumper anything 270 and up is fine. Bows work extremely well too and I have watched a good number of moose tip over when stuck with the pointy stick. It all comes down to shot placement and knowing your ability/limitations...maybe more so keeping to them. Moose certainly aren't as hard as one may believe to bring down given there size. With a rifle the furthest I have taken a moose is 225-250 yards, with a bow is 13 paces.

Bears same thing, they tip over very easily with a well placed hit. All except one of my bears has been taken with archery equipment at 20 or under yards. The one that I took with a rifle a 270 was used at around 75 yards.