I own a custom built pre-64 Win M70 chambered for the .257 Ackley Improved and it has been excellent on whitetail, mule deer and pronghorn antelope. I use 100 gr Nosler Partitions and the results have been super. I also have a .257 Weatherby Mag in a Mark V Euromark. I use 115 gr Nosler Partitions in it and a flatter shooter there isn't. A better sheep, goat, deer or antelope cartridge with the same trajectory and recoil hasn't been made. But the bottom line with any cartridge is shot placement with a well designed bullet... shall I say "premium" bullet.

I'm not a fan of the .243 Win but my wife shot a Sako chambered for it for years before going to the .30-'06. She
shot whitetails, mule deer and antelope with it using 95 gr Nosler Partitions.
Here's a pic of my 2003 antelope taken with my .257 Weatherby Mag and a 115 gr Nosler Partition.