I shoot the 140gr bergers in my 6.5 SAUM and the 156's in my 264 win mag. I'd agree with several guys that have posted in here about the speed threshold - if you're over 3,000 fps at the muzzle with the 156's I'd go that route. If not, stick with the 140's or even 130gr OTM's. In my 6.5 Creedmoor and 260 Rem I shoot the 130's at 2,600-2,850 fps and they kill impressively on deer sized animals.
The 156 in my 264 win mag at 3,125 fps is the single most lethal bullet I've personally shot at deer, coyotes and big hogs. With the 140gr hybrids and elite hunters in another rifle with the same speed, I had whitetail, hogs and coyotes running still after the shot. With the 156's, I haven't had anything take a step yet - they're almost shockingly effective on game in my experience.
I hunt in South Texas a lot and there's big hogs everywhere - last Thanksgiving I shot 5 hogs in the 150-250lb range with the 156's and not 1 took a step. They were mostly shot through the shoulders, lungs but a few were shot moving and they just crumpled.
I'm sold on the 156's above 3,000 fps.