Die cutting machines have 2 rollers, like and old wringer washer. The distance between them is fixed, so you can run something thru them that is thinner, but not thicker.
Sizzix dies are thicker than the Accucut go dies, so they will not work in the Go!.
Since the 2 dies are different thicknesses, accucut makes 2 different adaptors for the Studio:
this one for sizzix dies:
http://www.accucutcraft.com/cutting-...y-adapter.html
and these 2 for go dies:
http://www.accuquilt.com/studio-shop...or-studio.html
Since the Go dies are the thinnest of the three (go, sizzix and studio (wood)), the rollers have the narrowest opening, so it will only take Go dies (well you could probably get wafer dies to work, but they wouldn't be any good for quilting).
The Ellison big shot pro would take sizzix and go dies, but Ellison doesn't make an adaptor to use the go dies, but you could probably devise a shim.
I have had the accucut GrandeMARK (same machine as the Studio) since it came out 10+ years ago and have hundreds and hundreds (and hundreds) of dies from all manufacturers. let me know if you have any more questions.