The AR-10 variants will be the most accurate, consistently, pretty much hands-down.
Then everything else will follow in a highly subjective slug-fest propelled by loyalty to whichever guns people happen to own or like or wish they owned.
Some folks will have Saigas that will shoot into one MOA all day every day. Others will say the M14 is the most accurate of the second tier ... because the military uses it, or because of what accurized NM M14s/M1As can do. Some will consider condition of common specimens, while others will try to postulate based on theoretical accuracy of a perfect example, fresh from the factory.
If I had to make a grossly general statement, I'd say the Browning BAR (you are talking about the commercial/hunting rifle and not the old military squad automatic rifle, right?) will probably beat most of the others by a very slim margin because of being a bit more precisely made than most mil surp examples. Should be capable of 1-2 MOA or so. Some examples may be capable of better.
The average M14 supposedly edges out the average FAL by a slim margin because of bolt lockup design, but that's hotly debated. Call it a 2-3 MOA rifle, again, if not accurized, and not the Springfield Armory SOCOM-16 version which seems to exhibit poor accuracy by most accounts.
I'd probably put FALs, G3s, CETMEs at about the same rank. On average, 2-4 MOA performers.
Saigas might actually get a bit of lift by dint of the fact that they are, like the BAR, factory new rifles and have proved to be quite respectable.
All else being equal.
Of course, it is mighty hard to make "all else be equal." Feed an AR-10 cruddy surplus ammo and an M14 carefully tailored hand-loads and you'll get skewed results. And the same goes on down the line. Cherry-pick a very accurate example of any and it won't be representative of its breed (except for the AR-10s, of course).
So... YMMV!