Things aren't great between them, even outside Iraq. The Shia world is primarily non-Arab. They're a minority sect throughout the Islamic world and the majority faith in Iran, Iraq, Azerbaijan and parts of Yemen, Afghanistan and Pakistan. The Sunni dominate the balance of the Islamic world. Here's a map:
There is a bitter rivalry underway between al-Qaeda (Sunni) and Hezbollah (Shiite). Al-Qaeda leaders are said to be alarmed at the growing prestige of Hezbollah among the people of the Sunni M.E., especially after Israel's last failed invasion of Lebanon. There is speculation that this factor played a role in the Palestinian uprising four months later but there is no proof of that.
The tensions between Hezbollah and al-Qaeda are a threat to both of them but there is much that they share in common. Both believe that Israel must be destroyed. Here's the hook - militant Shia and militant Sunni believe the conquest of Israel will usher in the "End of Times" and bring paradise on earth.
No one is sure how this rivallry will play out in the next couple of years but is expected that the civil war in Iraq will have a ripple effect in parts of the Arab M.E. One thing that is certain: a lot of civilians are going to be caught in the middle of these extremists.