I use a load of a 130 gr Barnes TTSX bullet mounted to brass left-over from my tactical class .308 PRS rifle (which I use Federal Match in) and 47-ish grains of Varget ignited by some Remington primers. I went with the lighter, faster copper bullet hoping to keep recoil as low as can be on my CZ 550 rifle which has a 18" barrel, avoid meat damage, and keep lead out of my food.
I would say recoil is "less" but not much if I compare to a 150 gr Federal Non-Typical softpoint or something. If I compare to a 180 grain round, okay... the recoil is less. The gun is light and the barrel is short so... anything counts.
I've never actually done load development for this considering I rarely deer hunt past 200 yards and the load is always sub-MOA at the 100 yard range... so... not going to mess with something that works fine.
With copper bullets, you don't need the same grain weight as the regular lead core softpoints to do the same job.
My luck finding a deer to shoot is low, but this year I took a "bigger-ish" doe on some private land I got access to. She took the bullet, jumped up, ran 50 yards, and nose dived - conveniently - into a bunch of mud. Job done.