Most people think the beaver is better. I personally think the Manmoth is. Tame a high lvl mammoth, pump all melee, put on a ramp quetz, use exploit to your advantage = tons of wood with no effort. Beavers AoE is not as big, doesn't work on quetz.
get on a nearby hill or rock and kill ones you don't want as they usually spawn in 2s or 3s (recommend an argentavis). then start shooting the mammoth with tranquillisers. when it torpor runs finish it off, they are very slow so very easy to hit. (protect from dire wolves, yutiranus, etc....)