I think Auto Rifles should fulfill the "passive versatility" role. That means less flinch, recoil and fair handling.
I have a very good Horror Story for PvP that has Outlaw Snapshot. So it doesn't have rolls that change damage or playstyle at all. Even with all armor mods slotted and very fair performance as a player, it is still a bit quite hard to outplay opponents in PvP unless you catch them offguard.
From my observations in the past, Auto Rifles always suffer from 1 problem with 2 sides of a coin. One is, they don't deal really meaningful flinch to other players in PvP (even with HCR imo). The other is, that auto rifles still flinch a bit too much from the sides (which is regular behavior for all gun types). So, since Auto Rifles with High Flinch Infliction to other players isn't fun to play against, how about giving Auto Rifles the unique trait that they flinch less (from sides/behind) when shot by default?
That would make them more passively versatile in gunfights without making them stronger in TTK or other aspects that can break PvP alot. Also, that way Hand Cannon players (the arch enemies of all auto rifle players) can still have their playground untouched.
And for the players using all mods with Auto Rifles that would mean almost COD gameplay that some love so much with automatic weapons in that game.... Except for the recoil of course in Destiny 1 and 2.