It's difficult to say for two main reasons:

1. The non-Muslim (read: Christian) world was pretty much separated from the Muslim world.

2. Caliphs tended not to impose their personal religious doctrines on their populaces.

So to address the first point, there's no question that Islam expanded rapidly in its first few centuries. Once it stopped at the borders of Europe, the European world wanted nothing to do with their foreign neighbors and tried their best not to engage them in any way except for war. Of course there are some famous stories of Harun al Rashid sending an elephant to Charlemagne, but there wasn't a strong cultural exchange otherwise. To the Christians in Europe, the Muslims were heathens who were out to destroy the world, and to the Muslims, the Christians in Europe were basically barbarians without much to offer. So really there wasn't much that could reasonable happen in Islam that would make the European world care.

Secondly, and perhaps more importantly, Caliphs tended not to interfere with the religious teachings of their followers. Most governance was done locally, and Islamic jurists were disjointed from the government and created rulings in their own private schools. There were obviously policies that the Caliph enacted that were based directly on religion, but they usually didn't involve anything to do with the Sunni-Shia split. We see this in the fact that the Fatimad Caliphate, a Shi'a clan, ruled Egypt, a Sunni majority, without any major conflict based on religion. Saladin even allied himself with the Fatimads when it was opportune.

In these ways, the caliphs were kind of disjointed and the split was more of a religious one than a political one. The only exception to this rule was the Saffavid dynasty, which forcibly made its citizens in modern day Iran convert to Shi'a Islam. This included Sunni Muslims, Christians, and Zoroastrians among all the other religious groups that existed there. This probably doesn't relate to your question though, since these groups would still be considered part of the "Muslim world" since they lived in the heart of the Islamic Empire.

So I would say that the answer is: not much. Caliphs tended to ignore the religion of their populace and the split did not cause major conflicts for the most part. The Islamic world didn't suffer any major hindrances because of the split, and all science and military events would have happened exactly the same as they already did.