Dogger: I began using Rifles in 270 Winchester caliber back in the 1960's!
The 270 Winchester is a wonderful and efficient medium and big game cartridge - I know, I done'em!
With todays bullets and powders the 270 Winchester has just gotten better with time.
I also own Rifles in the other calibers you mentioned (30/06 & 280 Remington) and have taken many head of game with both of those as well.
IF... you don't have a Rifle in 270 Winchester then I heartily recommend you give one a try!
I have not killed a Moose with any of my 270's but I have killed Black Bear, Bull Elk, Mule Deer, Antelope, Blacktailed Deer, Mt. Goat and Whitetailed Deer with them.
In fact just 2 weeks ago I used my Remington 700 Sendero in 270 Winchester to harvest a very nice 10 point Whitetailed Buck here in SW Montana (130 grain Nosler Ballistic Tip one shot at long range).
I think if I ever break my "jinx" on drawing a Bighorn Sheep tag I would not hesitate to use one of my 270's on the Hunt.
The 270 Winchester does so many things so well and has so many attributes for the North American game Hunter that I think I better restate my previous "hearty" recommendation and upgrade that to to an emphatic "must have one"!
Best of luck to you if you decide to try one.
Hold into the wind
VarmintGuy
