Disclaimer - I'm not a hunter so I have no personal experience.
My dad took a LOT of deer at some pretty fair ranges (150-300 yards) with a Remington 760 in .243 and he swore by both the rifle and the caliber. He really liked it a lot and he was VERY good with it (though ya still suck with a pistol dad <grin>).
So it says something to me that he didn't even pause to select a bigger gun when he went on an elk hunt with my great-uncle.
.243 is a great round and you can do a LOT with it, but I think you also need to know what is outside the envelope for responsible hunting.