The main difference is that you can fully implement a 'Christian' values state and it isn't going against the grain to base it on mercy, equality, and not 'othering' those who don't agree. In other words a fully Christian society can fully implement the teachings found in the New Testament and not be considered 'radical' in any sense by a non-Christian living in that society. While it may be 'missionary' oriented it also wouldn't require exporting its philosophy. It also is comfortable separating civil and religious law - 'render unto Ceasar.'
Islam, fully implementing the Koran, is basically the opposite.
It requires fidelity at the threat of death and the forced conversion of outsiders. It requires civil and religious law to be the same.
Iran for instance instantiates the tenets of Islam in fact.
The Christian theocracies are basically historical dead letters at this point- and were mostly overlays on existing government structures:
The Roman Empire for instance continued to be Rome after the Emperors became Christian- it never really, despite the Pope's best efforts, become more than a light overlay on existing government structures, with King's utilizing theories of 'Divine Right of Kings' as a useful way to perpetuate their existing hierarchies. Even countries like Armenia that claimed explicitly to be Christian states aren't actually ruled by the priesthood- they have established national religions in many historical instances, not a truly religiously run state like Iran where the mullah's are the ultimate authority.
Rome/Papal States, Peter the great, Geneva/Calvin, some slice of the Byzantine empire, along with pre-United States Utah (and in a smaller scale the city of Nauvoo,) where you have had the clerical and government structures completely united in a Christian state that I can think of off hand. England in a much looser sense qualifies. And in these cases you generally again have, relative to Islam, a non-radical, especially as it relates to outsiders, experience.