The Slydini version begins with a single piece of rope (on the heels of cut and restored). This is cut into three equal pieces, which then become unequal. The kicker is when they are stretched back to equal length. Instead of all six ends being gathered together, the unequal ropes hang openly in the left hand. The right hand gathers three ends without bringing them near the other three, and yet the pieces are still stretched to equivalency. That's what throws magicians. For the finish, the ropes become unequal again.
The only weakness in the Slydini routine is that because it starts with one piece, spectators commonly demand that the three pieces be restored into one at the end. If the Conway routine lets me answer that demand without undue grief, I'm way interested.