I don't have the Big Kick, but have the Big Shot and the Westminster/Sizzix Big Shot Pro. I know that the smaller GO dies will not fit into the Big Shot, they're like 1/4" to wide. Now that's not to say that you can't use them in there as I've seen people on youtube cut that 1/4" off and use them in their Big Shot. (not something I did, just saw some of them demo'ed)
Go dies and even some Studio dies will work in the Big Shot Pro without having to cut any part of the die.