I think that the quality of ammo makes a huge difference but that is only in a rifle that doesn't have condition issues. You could shoot the finest match grade handloads out of my Mosin and still not get anything like performance out of it but that is because I ruined the barrel.
I guess it all depends on what you want out of it. If you were going to build a sniper rifle (I hate that term) out of it I would think having a good barrel to start with would be important unless you planned to re-chamber it... soo many variables.
That said a surplus rifle (Mosin, Springfield, Lee Enfield, Mauser) in good condition should be able to out perform the shooter everyday of the week.