RAIM
Don't forget the hand held units (at least the ones I know of) do not have the ability to do RAIM (Remote Autonomous Intergrity Monitoring) .. simply stated, a reality check that there is sufficient satellite geometry to ensure the required level of positional accuracy.
To fly an approach, one of the conditions for the GPS to switch to Approach Mode (+/- 0.3 NM CDI deviation), is adequate RAIM. That is required by the FAA TSO c129.