there is so much more to a teams performance than the side of the ball the coach is familiar with
Dungy definitely made his defensive stamp on the colts
This is going by observation and gut more than anything tangible (basically speaking out of my butt for a moment....) but it seems that coaches with defensive backgrounds are more apt to dictate the sytem and style of defense and then lean heavily on their coaches ... they may have a certain type of player they like, a certain scheme, value certain positions more than others - but come game day involve themselves with the game management, talking with the defensive coaches and frequently talking to the offensive coaches about what they are seeing the other defense do
the offensive coaches - especially the ones with the wizard or genius tag - seem to get a little bit more hands on with the offense, actively call plays, etc
on the whole I think this would allow the defensive background coach to be a little bit more honed in with the entire team
however, you do have teams like the ravens under billick that definitely weren't feared for their offense .... SF is very tough defensively but their offense is smart and efficient
definitely an interesting conversation - but I think in the end the coaches who do the best at establishing and managing staffs and setting a culture of success, accountability and work with a stable and competant ownership/front office are those that will have success - regardless of the on the field formula or their background