Mechanically, they are the same machine. The only differences are cosmetic.
I own the original Big Shot (teal and black, the new version is a hip and swanky pink and black. I have BS *envy* now . . . LOL!). I love my BS, tho. I've never owned the Sizzix, but, if I had, I would have upgraded to the BS or BK; they have a wider feed--6" and will accommodate a wider range of die sizes.
"So shines a good deed in a weary world." -Willy Wonka