Brad,
I have yet to find the higher sectional density of the .270 with equal-weight bullets makes any difference in killing big game--and between Eileen and I we have taken a bunch of animals with both over the decades, in both North America and Africa. What does make a difference is bullet construction, per usual.
With cup and core bullets, of equal construction, the higher SD bullet may not kill any better, but they will absolutely penetrate deeper (270/150 vs 308/150).
