Islam is no more inherently violent than Christianity has been in its past.
It was under Islam that Jews were able to escape Christian violence and persecution during the middle ages. During the middle ages, while Christians were brutally persecuting Jews and waging holy wars against a flourishing Muslim empire, said Muslim empire was a center of science, philosophy, education, literacy, the birth place of the alphabet I'm typing in right now, etc.
Christians killed, tortured, terrorized, and exiled hundreds of thousands of Jews, and Jews who were forcibly converted, during the Middle Ages and during the height of the Spanish Inquisition.
And this sort of thing went on for about a thousand years, starting from around the days Rome converted to Christianity and began passing anti-Jew laws, and it didn't really subside until the secularization of Europe began towards the end of the 17th century.
Holy wars, mass forced conversions, massacres of entire Jewish ghettos, torturing/burning said people who were forced to convert because they may have been living as secret Jews. Not to mention the mass exiles.
I don't know enough about the contents of the Quaran or the Bible to talk about whether Christianity or Islam is inherently violent or peaceful. But as an ethnic Jew who spent the last several months learning about his heritage, I can tell you that historically, Christianity has been at LEAST as violent as Islam has been in all of its history, if not moreso. Whereas Christianity has sought to make war with, convert, or expel "heretical" religions within its borders, Islam has typically been tolerant, especially when it came to the People of the Book (Jews and Christians) who were allowed to live with a relative amount of freedom, merely being subjected to special laws that barred them from certain professions and taxed them more, among other things, rather than forcing them to convert through torture or threat of death. A similar thing happened in India, when the islamic Moghul Empire conquered most of the subcontinent, bringing an entire population of Hindis under its rule.
That isn't to say Islam was perfect. I read about at least one massacre of Jews at the hands of Muslims, and whenever a Muslim empire was on the decline they would typically take it out on their Jewish and Christian subjects. But they never went as far in scope of brutality as the Christians did.
So, regardless of what either book says, Islam hasn't really been any worse than the other major monotheistic religion.
