When I go from the hoods to the drops riding the trainer my cadence increases along with my power. It just feels easier but I think that is due to my motor pacing and training at the track. Typically, we race in the drop and may go to the tops during easy efforts or warmup. Here is a pic from 2010 Track Worlds 45 to 49 points race. Note that everyone is in the drops and the position is about the same. When the pace is full on the racers bend their elbows.
AZT, I assume you race your crits in the drops.
My ability to hold power in the drops is very good but when I switch to the TT bike it is more difficult to make power with my arms in and with a more severe hip angle. It is also easier to make power if I drop my head since my shoulders and neck muscles relax but I cannot see well.