The .303 is an adequate round for deer and has killed LOTS of moose and elk , along with about every other species of game in the world, since it was the standard military cartridge of the British Empire for years and years...

That being said, it's not as powerful a round as the 30-06 or the .308, although it's probably every bit as capable of cleanly taking game animals within it's useful range of perhaps 200-250 yards..

Recoil would be similar to the .308, and a little less than the 30-06 with equal bullet weight and rifle weight..