They are less effective then before 1.6 patch.
More precisely, -50% effective.
Just checked in my current Sassanid campaign I started playing.
For example, if two levies would give 20% of public order in some city, two peasant units would give just 10% public order instead, although both type of units are of same stack size.
This is new behavior after the patch.
I suspect that's what for "is_peasant" flag is used in units data files. To mark low public order capable units (all peasant units in this case).
I guess this could have some use in future modmaking too.
Not to mention that some of old strategies will becomes less effective.
P.S.
This is Barbarian Invasion campaign feature only.
Imperial campaign peasants behave normally (nor they have "is_peasant" flag).