RE: Bullet Damage...
The problem with answering your question is, we don't know the exact construction or velocity of each of the bullits you asked about. So, all of the answers can only be "general" in nature.
In most cases, the 243 will go through animials of that size, as will the 22-250 with any of the heavier bullets.
The 22-250 will have a bit less recoil, and will be a little cheaper to handload for.