I hunted with a 20" 308 last year and took 3 deer with it. AR10 even. I also had a Husqvarna with a 20" barrel in 30-06. I liked the Husky, but it wasn't the greatest with the short barrel.
So my first choice would be a 308. Second choice, if you feel the need for speed, would be a 300RCM. The cartridge is designed to deliver magnum performance in a short action just like the WSMs, but will do it out of a shorter barrel, like the 20" you are looking at. Third would be a close look at the 30TC. 30-06 performance out of a short action. I don't know how it would do with a short barrel though, all the TC Icons come with 24" barrels.
I would like to see DPMS chamber ARs in the RCMs as well as the the 300RemSAUM. An AR10 in 338RCM, how cool would that be? I know ArmaLite is now or will be soon offering an AR10 in 338 Federal.
Just my thoughts.