I asked this very same question from the folks here not too long ago, but I was mostly concerned with Elk hunting capabilities. Got a lot of great responses, the most common being to go with a 30-06 in a semi-auto format. I was all set to do just that. Had one picked out and all, but I spotted a beautiful Winchester Classic Featherweight in 30-06, so I got it. I think I will like the lightweight aspects of the rifle, especially packing it around all day. And I hope it doesn't beat me up too badly in the recoil dept.
Having said that, I think I would go with the 6.5x55 Swede, especially if you don't have larger game in mind. I have heard a lot of great things about that cartridge and its capabilities, from a lot of experienced hunters. Some have taken some pretty tough critters with that round and they are extremely pleasant to shoot.
(Nice dig, Pointer, on the 270.)