The Good News Bible focuses on the New Testament out of embarrasement at those ideas. The old testament has been used to justify slavery and as you pointed out, genocide.
I think any comparison between the religions should include Judaism as it is their story you are referring to directly. That Christians used it is fact. They dont use it now. Muslims have a far more violent beginning the Christianity. They conquered to spread the word, wheras Christians were feared for being pasifists who wouldnt defend the empire.
That soon changed. The wars in Italy turned the Pope into a lord of the realm and he instituted wars with great enthusiasm at a time when Islam had fought civil wars and was becoming an advanced centre for learning. The Jews never had any power after the dispersion and were thrown out of europe depending on how much money they had lent the local christian king.
The more they lent, the more likely they were to be repaid by exile. They were almost always taken in by the muslims.
So historically, the religions of the desert are all tainted, and I dont think anyone can claim superiority over another. They have all had their turn at violence.