From my discussions with a number of owners, the long barrel VEPR in either .308 or 7.62X54 can do about 1 1/2 MOA with Match ammo at 100 yards new out of the box and easily stretch to 500 yards. Some are owner set up as SVD style "sniper rifles" as well and look and shoot well as such. In Russia they are well regarded in their various hunting stocks and thumbhole stocks for big game.
This accuracy is nearly comparable to my much more expensive SVD and perhaps better than my new R25 GII in .308. The SVD with top ammo does 1 1/4 to 1 1/2 MOA, maybe a little better on good days, but with top ammo only.
All this depends what you want to do - real superb bench accuracy, rapid fire capabilities, hunting, zombies....
A PSL is a much more questionable item - each is different as one-off put-togethers and you probably don't want to take it deer hunting. Some members do great shooting accuracy with theirs and some don't. Some are very reliable and some are not.
I personally would take the VEPR as a hunting and plinking and SHTF rifle quite happily in either .308 or 7.62X54R, with the Russian round my favorite if I got the longest barrel. I can reload, so anything is possible in ammo.
This is not quite as good accuracy-wise as a quality bolt gun like a heavy barrel Remington 700 or a new Savage at 500 yards or more, but they can't fire 10 rapid repeat shots quite so quickly if you need that.
My rather expensive and time consuming solution has been to own several varied rifles, but the accuracy queen is a long and heavy barrel Remington 700 .308 that I have built up slowly with a Bell & Carlson sniper stock, new bottom metal for 10 round mags, a Harris bipod, a new Timney 1 pound trigger and other such goodies, topped with a Leupold scope. Now that can hit small stuff all day at 500 yards and has been done slowly so my wife hates me less for it. Too heavy to lug around in the woods for long, though.