It's largely cosmetic, Geno. The 700 and 800 are older models, the 850 is newer.
There is a slight difference in the feel of the buttons; the lettering on the buttons are different fonts; and the back-lighting is different. On the 800, the buttons themselves and the screen light up with a greenish glow. On the 850, the lettering on the buttons (not the buttons themselves) and the screen light up with a lighter color.
The "select" button in the middle of the joystick is a completely separate button on the 850. On the 800 it's a part of the joystick itself. Other than that, the remotes pretty much do the same thing. Because of these differences, the 850 is slightly more user friendly. Only you can decide if that is worth extra dough.
