have had both a 6 MM Remington in a single-shot Browning B-78...the most accurate rifle I have ever owned, about 1/2 five shot groups at 100 yards. Killed a lot of deer with it using IMR-4350 and an 87 grain Hornady varmint bullet. I expected the varmint bullet to "blow-up" and shower the vitals with bits and pieces of the bullet however, in actual practice, (I always did a post-mortem), the jacket would separate from the core and usually stay in the chest cavity whereas the core would exit on the off-side causing a quick kill.
Also owned a circa 1976 Ruger M77 in .257 Roberts. The Ruger had excessive freebore, could not get anywhere near the rifling with the longest bullets. It got spooky when working up loads inasmuch as there were never any pressure signs, even way beyond max data published in the loading manuals. I finally backed down, for safety's sake. I killed a lot of deer with that rifle also using a 120 grain bullet (cannot remember the manufacture of the bullet now), before gifting the rifle to my son.
In all, they both killed deer efficiently and I could not realistically see any difference in their performance. However, it should be noted that I always shot the deer behind the shoulder, where there is but ribs to resist the bullet.