PROM greater than AROM
It is quite normal that the clients can move their body parts a bit further in PROM than they can in AROM. This has most likely to do with the fact that the muscles are not contracting very well when they are completely shortened in full inner range.
AROM greater than PROM
Sometimes however it happens that AROM goes further than PROM, like in the case of dorsiflexion of the foot, where a passive movement is sometimes more difficult than an active one. In the case of strong calf muscles it might be that antagonistic inhibition of the calves will prevent sufficient passive dorsiflexion.
Another reason for AROM achieving better results than PROM are trust issues. The client knows that they can stop their AROM movement any time it’s getting sore. But do they trust you to do the same? They will (often subconsciously) guard the area and build up resistance by contracting their antagonist muscles.
It is of utmost importance that the clients are assured that all movements will be performed slowly and that they will have sufficient time to say stop. 
TIP
Move their body part a little bit in a pain free range, slowly increasing the motion. Once they see it does not hurt they will be more likely to relax.