Well, one thing that always bothers me is the fact that anyone can make fun of Jesus on tv or in films, but mention Mohammed in a negative way, or even show him at all and riots break out.
What are the issues Christianity and Islam face when they clash/together?
The issue is that neither group is following the admonitions found in their respective holy texts. The Bible says "Be peaceable with all men" (Romans 12:18), and the Qur'an says "Fight in the way of Allah those who fight you but do not transgress. Indeed. Allah does not like transgressors" (Surat Al-Baqarah 190). So if there is no aggressor then there can be no retaliation. The issues come in when the followers of these camps misapply their texts as instruments of hatred and as justification for vile acts.
They both suffer from supernatural, myth infatuation. Look at it this way though, they both are more comfortable with other people who believe in a bunch of fluff, than they are with people who don't believe any of it. That's why they both hate people like me more than they hate each other.
Jesus may not be more than just a prophet, they say, but at least those infidel Christians advocate for a fairy tale of their own. Those Muslims may be a bunch of terrorists, they say, but at least they also believe in a magical afterlife.
Atheists, now.....
You use the term "Christians" very loosely. Christians are taught to "love their enemies" and not to engage in carnal warfare. Matt 5:4 and 2Tim 2:24 says "a slave of the Lord does not need to fight, but needs to be gentle toward all, qualified to teach, showing restraint when wronged "