This debate has been in session for a long time.
Between those two options, the ballistics are conclusive, 6.5 Creedmoor is a superior bullet. Will you notice the difference? Yes, approaching 300m range, you certainly would, it's undeniable.
I can't think of any reason to select 308 over 6.5 Creedmoor, for stalking in the UK. Any such arguments can, I believe, be satisfactorily debunked.
I think I've seen all the arguments on both sides, but I retain an open mind if somebody wants to teach me something new.