Mayday - imminent danger, immediate action required: depressurised so need immediate descent FL100.
PAN - now we are at FL100, we are out of imminent danger but still require priority handling/approach.
Mayday = pilot can choose any airport, any runway, any direction PAN = pilot can choose any airport but ATC state which runway for landing.
Mayday vs PAN - other than mentioned above, ATC would do very little differently. IF there was a Mayday and PAN heading to the same airport within similar times, the Mayday will probably go in first (I have seen the opposite but for very good reasons)
Mayday = I'll get you the most direct route possible including through any active danger area PAN = I'll get you the most direct route possible however may go around some danger areas that co-ordination may not be possible to achieve to transit.