Denton,
I have seen many pronghorn fall to a .243. Two this year alone, one at 175 yards the other at 210 yards both distances measured with laser rangefinder before the shot. I will admit both of thoses were close shots for most antelope hunting. So I guess it depends on how close you think you will be able to stalk. I will admit the most common antelope gun in this area is a 25.06 which will have a greater reach than the 243.
I also saw 2 elk harvested with a .243. The first a large 6 point bull scoring 351". The first shot 245 yards the bull hunched up went about 20 yards and layed down. Second shot at 75 yards to finish. I saw a cow elk shot at 200 yards front legs collapsed and it tipped over. These were all shot with the same gun by different members of the family. They were using factory shells, Hornady Light Magnum 100gr BTSP Interlock Bullet with muzzle velocity of 3100fps. All shots actually passed thru the animal except for the bull at 245 yards which I have had my 7mag not pass thru at that distance!
Its all about proper bullet selection I have seen too many guys go out with a 243 with light bullets designed for light skinned game or even varmints and wonder why it did not penetrate the elk shoulder.
You also have to be able to put the bullet in the right spot!
Ask any fish and game officer and they will tell you the tiny little 22 mag has killed more deer and elk than any other caliber. Illegally of course, but the animals are still dead.