The Catholic Church is less liberal than your church. We don't allow use for contraception or abortion. The Catholic Church declares homosexuality to be a sin. The Catholic Church takes a dim view of Divorce and re-marriage, and actually teaches you are not allowed to divorse. Catholic Church also doesn't hold to marriages outside of the Church. It doesn't allow for invitro fertalization. And is conservative on just about every political issue.
On the Other hand The RCC/Orthodox Churches are the original Christian churches.
When compared to Islam, there is a good chance that Islam may still be greater. Looking at one of the sites that broke down "Christianity" down either further, Christianity includes all of those who deny Christ as deity.
Now, Islam would never include anyone that would deny that Allah is the only God and that Mohammed is his Prophet. That is their creed. You cannot be a Muslim without believing that.
Christianity is a follower of Christ. But if it is not the Christ of the Bible, at least that Christ is deity, the second person of the triune Godhead, then who is the Christ that they are following? How much of "Christianity" would be eliminated?
It would eliminate all the cults--those that believe he is just an angel, a man, a prophet, another god, etc.
It would eliminate most mainline liberal religions that no longer believe he is deity.
It would eliminate all the "Benny Hinn" types who believe that the trinity has nine persons, not three.
After one eliminates all those who either deny the trinity or deny the deity of Christ, those who call themselves (even if they are not born again), would be less than those that call themselves Muslims, even if they are not devout Muslims.