Hello...
well...in our company we keep the APU on during the turn-around...and we don't use EXT-PWR at all. in fact, we use the APU all the time unless the aircraft is day-stopping or night-stopping (aircraft on ground for 6 hours or more) where the engineer shut's down the APU once he's done with his checks.
we are doing this policy since a very long time , but that doesn't mean we didn't have any problem with the APU's ... sure we had.
i think it is better to use the APU since it has more stable current than the EXT PWR ( in terms of supplying the aircraft systems ) ...and i stand to be corrected .
regards