There is one big difference between an Islamic versus a Christian theocracy, which is that only the former is utterly intolerant of unbelievers. A Christian theocracy will mostly leave an unbeliever alone except in the context of abortion, evolution, and some mixing of church and state. In contrast, an Islamic theocracy will likely get an unbeleiver beheaded. The degree of oppression is not the same.
Historically, the opposite is true.