Both have multiple schools, so that is a very broad question. I think the most interesting direction to take it is to look at philosophical differences. But even that is much too broad to answer. Also these philosophies are seldom if ever representative of theological orthodoxy.
Historically and very broadly speaking, Sunni philosophy could be said to be more Aristotelian or peripatetic (Ibn Sina, Falsafa) and Shia philosophy more platonist or neoplatonist (Ismaili Shia). But that's a huge oversimplification, since there is a huge overlap, especially with Aristotle, since Ibn Sina is sometimes claimed by both. Both are connected to different mystical Sufi traditions. Shia has Illuminationism and transcendent theosophy (existence over essence, Twelver Shia, Mulla Sadra). Sunni also had Averroism (Ibn Rushd). Ibn Rushd and Ibn Sina (Avicenna) together strongly influenced almost all medieval European Christian thought and scholasticism.
If you want a good overview, you can listen to the 75 episodes of Peter Adamsons podcast "History of philosophy without any gaps" on philosophy in the Islamic world.