Not sure about handloads but factory 30-06 is bugger all faster (<100fps) than a 308 with 150g or lighter, just less efficient and makes a bigger bang doing it.
I noticed a fair bit more recoil from 270 than 308 firing them back to back, haven't met many people who would suggest otherwise! Not a problem for some of us, but I can see how it is an issue for others.
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