Chris,
I know the 781 quite well...have lived with one for a couple months now and am also quite familiar with it's design from technical standpoint. It's a clearly obvious step forward from the 581SE the second you hear it, I definately would recommend updating your 581SE to the 781 level if you have the means to do so. You won't regret it.
The 781 uses a completely new and different power supply topology and it really takes the unit to a new level. There are other differences as well but the power supply change is the big one. As everyone knows, the power supply is the foundation for good sound....the 581SE is no sloch in that department, but this is in a different league.
Hope it helps,
Steve Huntley