I have both also. The two cartridges you picked are my two favorites(other than the 280 Rem) but if i had to choose one over the other, it would be the 270.
I like the flatter trajectory of the 270. However, the difference between the 2 on the business end is nominal. I've never been Red Stag hunting in New Zealand, but I have been there and I have to assume it'll be like Mulie hunting. Longer range shots are definately the 270's milleu. However again, ballistically they're really close. the 270 with 130gr will reach out and touch someone. A last bit of advice, Practice, practice practice. You make more of a difference than cartridge choice.