To look at Christian history, it is hardly conceivable that modern, prosperous, relatively peaceful nations would exist today. Christians "evolved" from brutal zealots to modern, peace-loving people.
You also can't look to the Bible for the source of this peace. The Bible is filled with social rules, prohibitions, and punishments that are barbaric by modern standards. If Christians don't judge the Bible with modern sensibilities, why do they judge the Quran with modern sensibilities?
If we judge the Quran to be more violent, you have to consider the times in which it was written. The Quran was written in the 7th century, which was an extremely violent time in human history. It was written down as events unfolded.
On the other hand, the old testament came from oral tradition passed down for thousands of years, and finally written down when writing became possible. Before it was written down, the stories likely changed. Over the course of thousands of years, much of the violence was probably lost in the oral transmission. The new testament was written during the time and geography of "Pax Romana", a time of relative peace in human history.
One of the most peaceful religions on the planet has holy books that are much more violent than the bible or the quran. The Hindus have the mahabharata and the ramayana. The Hindus have managed to become quite peaceful. Perhaps they take lessons on the evils of violence from these books. Is it so inconceivable that Muslims could do the same from the Quran? Many do, actually.
Christians have modernized and moderated through education, prosperity, and learning from the mistakes of their ancestors. Christianity has gone through enlightened / peaceful periods, and fell into violent periods of regress. Islam has enjoyed many enlightened /peaceful periods.
Islam is emerging from a violent period of regress. Just look at the progress of women's suffrage in the middle east to see how rapid this emergence is happening. Christians live in a nascent period of enlightenment. It wasn't so long ago that Christians were violent and aggressive toward "pagans", "heathens", and "savages".
If history has any lesson for the modern world it is this:
Enlightenment, prosperity and peace are fleeting and fragile. These ideal states of human existence are easily disrupted by violence, aggression, and war. If we wish to live our lives in, and pass on to our children this ideal state, we must stop vilifying each other. It is imperative that we start building cultural bridges and break down the barriers that divide us. We can pass on to our children a culture of enlightenment and peace. We just have to set aside our hatred and mistrust.
