Got a little confused here, since you were talking about the .30-06, which also can be loaded with the 165 grain .308 bullet. Especially when you then mentioned the Winchester 88. But with the additional information I figured out that you were talking about the .308 Winchester cartridge.
A slight correction if I may; the Winchester 88 first came out in 1955, not '53. I have owned 3 of them over the years; my first one was from the first year of issue. All were exceedingly accurate giving me MOA groups (off the bench) with a Lyman Foolproof rear sight using the smallest hole aperture available and a Redfield Sourdough Patridge up front. Unfortunately my eyes don't work that well anymore to shoot that well. But I kept the family in meat all the time I was in Alaska.
My CF rifles now are a Marlin 336 I bought a while back and had bored out to .38-55 by JES Reboring, and a H&R 058 in .30-30. I just picked up another barrel for it with plans to send it to Jesse to have him make me another .38-55, as I just don't feel comfortable with the new Marlin and love the H&R.