Two good choices
You have two good choices there, I've hunted a few antelope in western SD and they are the two choice I have as well, also a .308. If you are a good stalker, a 300 yd. shot shouldn't be hard to get. I've shot my biggest goat, a 15 1/2", with a .243 at 75 yds., he thought I was a challenger and he just kept coming in. If you look at tables and yadda yadda yadda, you'll see that the .243 with a good 100 gr. bullet at 3000 fps. is no flatter than a .30-06 with a 165 gr. at 2800 fps. Either will do the job, just make sure the .243 has a Nosler Partition in it, you'd hate to wound an animal, and a 150 gr. or 165 gro. Nosler BT will be great our of the .30-06, shoot whichever bullet your '06 prefers, mine likes the 165, so that's what I feed it. Good hunting!
PS You don't need a magnum!!!