I disagree. You are equating apples with oranges imho. I would challenge you to provide some verses from the Bible which teach that killing Muslims is a service to YHVH. I would also challenge you to find verses that suggest that Christians or Jews should expand religion militarily to other nations (outside of Israel). These verses just don't exist in the Biblical text yet there are many verses in the Quran and Hadith which literally teach Muslims to do this.
The Quran and the Hadith were not used in the "same manner" at all. They are not verses "cherry picked" and distorted out of context. There is a very obvious mandate throughout the Quran/Hadith to literally expand the religion through warfare. Also, the premise of Jihad is openly praised and encouraged as one of the highest forms of Islamic duty. Many modern Muslims suggest that Jihad really means "inner struggle" and try to distance these verses away from literal violence. I am very happy that people are willing to look at these verses this way but that doesn't mean that something is actually true. The more contextual approach to both Islamic texts is that the literal expression of Jihad is what the author traditionally meant to convey.
This is part of the reason for why Christendom has been able to reform over these years as opposed to much of the Islamic world. The Bible simply lacks the literal verses which suggest this type of religious expression where the Muslim world, especially the moderates, have to deal with these very violent verses. This is the root problem. Islam is difficult to reform because of these challenging verses which can't be avoided.
Sahih al-Bukhari, Volume 4, Book 52, Number 177:
Narrated Abu Huraira:
Allah's Apostle said, "The Hour will not be established until you fight with the Jews, and the stone behind which a Jew will be hiding will say. "O Muslim! There is a Jew hiding behind me, so kill him."