I want to try to make this as clear as possible so I'll break down the two routines:
1. Hand a cube to a spectator to be mixed (Cannot be done with The Enchanted Cube)
2. Pull out another cube and show that the cubes match perfectly (Cannot be done with The Enchanted Cube)
3. Optional ending: Slowly solve the mixed cube with one hand (Cannot be done with The Enchanted Cube, but is taught if you want to introduce another cube to The Enchanted Cube routine)
Enchanted Cube Classic Presentation
1. Show a mixed cube. Toss the cube into the air and watch it solve itself (Cannot be done with Rubicon)
Enchanted Cube Greg Wilson's Presentation
1. Show the mixed cube, toss it into the air and it solves itself (Cannot be done with Rubicon)
2. Introduce another mixed cube (this is not the enchanted cube, it is a normal cube that has been specially prepared) and solve it with one hand. This one-handed solve is similar to the solve in Rubicon but similar solves have been used by Garrett Thomas, Takamitsu Usui, and made popular by Stephen Brundage.
3. With a mixed cube in one hand and a solved cube in the other, you toss both cubes in the air and both cubes become solved (Cannot be done with Rubicon)
As you can see, the tricks are completely different. Rubicon is basically a piece of mentalism. The Enchanted cube is a quick visual piece of magic.
Here is a video that I made underlining the differences: https://www.youtube.com/watch?v=9S-YMgwc9Ns&feature=youtu.be