Quote Originally Posted by Antaresia View Post
better video

http://www.youtube.com/watch?v=ILDvDP5tHtg

forward is fine, reverse is not.
The cassette isn't freewheeling backwards freely. When you pedaled backwards, the cassette would stop turning, the "top" (lower in the video) run of the chain would get very slack, the derailleur cage would pivot thus feeding chain to the crank, and finally the increased derailleur tension was enough to turn the cassette briefly.

When pedaling forwards, the chain transmits enough force to overcome whatever drag there is on the cassette.

I still say that the rack mount hardware is dragging on the cassette.

A test: Roll the bike backwards. This will turn the cassette backwards with the full force of the rear wheel's turning. The chain should run backwards and the cranks should spin backwards. I suspect it will run "smoothly".

If you don't mind getting your hands greasy, reach in (the non-moving bike) and spin the rear gear cluster backwards. For comparison, do this on both your bikes. I suspect the new bike's gears will be much harder to turn.