Not sure if I have this right..
An active probe is single end amplification and cable driving.
A differential probe is differential amplification and cable driving.
Only the differential probe can provide attenuation to CM noise due to the Earth ground loop.
Probe -----------| Line powered DUT --------------| scope -----------| | + DUT com | ~ | ~ | Coupling Earth to Earth
Fig: Passive 1x probe showing earth loop.
But, if a scope is battery powered, an active probe is good for best performance.
D from BC