Well, having collected only one antelope, I can't say as I have a "favorite". I used my '06 on a quartering frontal shot; hit him just inside the point of the right front shoulder with the exit just behind the left shoulder. 100, at most 125 yards.
He just crumpled in his tracks.
I had my '06, since I was hunting in front of strangers. It's one thing to goof in front of buddies; just makes for good campfire tales. But in front of strangers?
On that shot, in that situation, my .243 would have been plenty good. As I have read. But to get back to the original question, a .270 would have done just fine, and out to 300 yards equally fine.
The more important thing, overall, is that it was good people, a beautiful day, lots of antelope around, and a few nice mule deer bucks. And the taxidermist stretched the hide over that shoulder-mount, where he looks like he would have dressed out around 150! (He was probably 90 to 100, on the ground...)