I'd say an air compressor would be called into service a lot more often...but there is no reason both cant be run off the same engine either,its just the amount of room under the hood that will limit that possibly...
A weldenator CAN made very good welds,depending on how it is set up--if you use the DC output it will weld a lot better than a typical AC buzz box home welder,some guys use the three phase AC right off the stator bypassing the recitifier and diode trio and weld with the highrer 3 phase AC cvoltage,which is a lot more hazardous,but the high frequency makes for a lot better penetration and puddle control..