The 6.5 bullet has killed hundreds of thousands of NAATZees, commies and anyone else who crossed the frontier uninvited.
Same could be said of .30-caliber bullets.
that same bullet is used for large mammals of the 4 legged kind extensively in Europe.
Frankly, the 6.5 is probably better than the 7.62 at killing mammals.
6.5 is going to vary greatly on the cartridge the bullet is supported by. A 6.5 Grendel is going to be crap compared to the 6.5x55 Swede that you are referring to indirectly.
As far as 6.5 being the better killer, I wouldn't say one or the other is really a big difference in anything in Texas. Hunting animals (people included) has more to do with shot placement than anything else.
It also offers better BC for long range shooting.
MUCH better BC's in the 6.5mm world than any realistic .308 load.