The original statement was that the Koran is more violent than the Bible.
In reality the Bible is far more violent than the Koran is.
The original statement did not say that Islam is more violent than Christian doctrine is. However, the Christian doctrine (New Testament) does reference destruction and killing more than the Koran does so by that standard Christianity is more violent than Islam.
"Killing and destruction are referenced slightly more often in the New Testament (2.8%) than in the Quran (2.1%), but the Old Testament clearly leads—more than twice that of the Quran—in mentions of destruction and killing (5.3%)."
A software engineer analyzed the Quran and the Bible to see which was more violent — here's what he found
The difference between muslims and Christians is that when muslims go off the rails they engage in limited atrocities. They act as individuals or in small groups. They become loud and obnoxious and the fanatics force the others to act submissive.
Christians, OTOH, engage in violence on an industrial scale and once they start killing will kill tens of millions without a second thought. They don't tend to become hysterical and start yelling about it. They just get busy and start killing.
So, when muslims get pissed off a few will go on a rampage and kill a few people. When Christians get pissed off they will stay calm and kill an unlimited number of people without a second thought or any remorse.
Read history for examples.