When well glassed in, the 1-piece stocks I saw back in the 70's seemed to give very credible accuracy - with handloads - in the #3's, but I do not remember them being particularly better than 2 piece stocks.

I have 2 #4's that shoot exceptionally well with the 2 piece stocks (one military and the other a factory sport stock) and see only 2 reasons to change them. both rifles will make 1 1/2", 3 shot groups at 100 meters off bags - factory peep rear and blade front. The 2 piece plastic stocks have better length of pull as well as 'feeling' and 'looking' more like a rifle you'd want to hunt with. They actually look pretty good- and are not expensive - $75.00 I think will fit both #4 and #3's - sometimes with slight modification, sometimes drop-in.

A friend of mine has just finished up his fall hunt with a #4. Keith's load was not excessive for the .303 chambered #4 & custom .308" barrel - something like 45gr. IMR4064 with a .308" 150gr. Interbond @ 2,740fps or so. This fall, he shot 1 bull moose, 2 deer and a bull elk with that load - with picture perfect expansion, exceptional retained weight (140gr. average) and very impressive penetration, with exits on the deer. Sounds like a good tough bullet.
Oh yes - 2 piece plastic stock.
I should add that Keith is the best game shot I have every seen. The elk was well past my self-imposed limit of 300yards, yet the .303 did the job - 3 steps and dead.
Another great old round with no flies buzzing it's carcase.