It's complicated.
There are no major theological differences as such, just a large number of minor differences that, for the most part, don't follow any specific pattern. The reason for this is that the Sunni-Shia divide was originally a political conflict over the leadership over all Muslims. The Shia position was that the Prophet Muhammed had bestowed on Ali ibn Abu Talib and his line of descendants a divine mandate to rule. The Sunni contest this, and consider the matter of leadership not to be a religious matter in the first place, that Muslims are free to choose their own leaders.
Over time, though, the two factions developed their own separate theology and ethics. This is part from having different scholarly traditions, but also due to differences in hadithology. The hadiths are the Islamic secondary religious texts, preserved narrations of the life and acts of the Prophet Muhammed and the early Islamic community. Thing is though, there's an immense body of such narrations, the great majority of which is considered apocryphal. Which are authentic enough to serve as the basis for the religion is a matter of difference between Sunni and Shia, mainly because there are a number of prominent characters in early Islamic history whom the Sunni consider to be honourable companions while the Shia consider them to be crooks who usurped leadership from Ali, and thus reject any narrations tracing back to them.
Most of the current Sunni-Shia fights in the world, though, have little to nothing to do with theology, the question of leadership over the Muslims, or even the choice of state religion of a country. Most are simply intercommunal power struggles, much like the Northern Irish conflict. The days of Shia attempts to create a Caliphate ruled by a Caliph with the right line of descent from Ali are long gone. Iran, the world's only real theocracy, is rather structured around a rather newfangled revolutionary idea of a mix of clerical rule and democracy.
