Antelope are very curious animals. When I first moved to NM they were everywhere and when you set up to work you would soon find many within 30-40 feet of you standing and watching. Those days are long gone with hunting seasons making them much more shy and long term drouth having seriously reduced their numbers. During my working days I had to keep close watch to keep from running over one. THey had a tendency to appear from nowhere and race you to cross the the road in front of you which got one ran over frequently. Now I hardly ever see one when out prowling around on that road.
They are lightly built creatures and if using a 270 I would pick the most accurate load for my rifle as shots are now going to be at some distance and any weight bullet will get the job done as long as it is put in the right place. Personally I consider 270, 308, and 30-06 overkill for these animals. I never had desire to shoot one back when I hunted. It would have been too much like driving out and shooting a cow because of their lack of fear of man at that time. I once pulled off the highway to watch two of them chase a grey fox ragged round and round in a circle and I wasn't 30 yards from then and they paid no attention at all to me. It was in the spring and I figured the fox had made a try for a baby that was hidden in the grass.
Back when they were plentiful I would see them in hot summertime standing one to a high line pole, nose to the pole, and their body in what little shade it provided.