I don't really have the necessary knowledge to properly inform you but I believe I may be able to guide you in the correct direction and I am willing to be corrected.

There were some significant differences between the Umayyad and Abbasid caliphates. Indeed it was these reasons which caused the Abbasid revolution and their succession of the Umayyads.

It is important to understand that the Umayyads were not particularly interested in the conversion or assimilation of religion or culture from the lands they conquered. Indeed the Ummayads regarded Islam as a religion just for Arabs. Additionally, most Arabs of the time, including armies lived apart from their populations. Basra and Fustat were cities founded by Arabs to keep apart from the conquered. Arab culture, primarily tribal was maintained and there was no desire to mix paternal bloodlines with conquered people.

What did interest them however was the wealth of taxes the affluent Byzantine and Persian provinces gave them. Under Islamic law Muslims are obliged to pay a tax, 2.5% of their annual wealth known as Zakat. Similarly, non-Muslims pay an annual tax, though of higher percentage than Muslims called Jizya.

As more of the Ummayad empire's population converted to islam, the Ummayads found their revenues decreasing, as people paying the higher tax bracket due to Jizya, were now paying Zakat. Gradually, the non-Arab number of Muslims outgrew that of Arab Muslims but this did not change any of their social conditions. Non-arab muslims were still treated with contempt, still forced to pay Jizya rates of taxation, still forced to live apart from Arabs and still seen as second class citizens.

Since the Ummayads were Arab minority rulers in their own empire it is unsurprising that through discriminating against most of their population, they became unpopular. This discontent was most pronounced in Persia, were the Ummayads were persecuting Persian-speakers and Zoroastrians.

When the Abbasids finally rebelled against their Ummayads and replaced them, the weight of non-Arab muslims, non-muslim, Persian, Berber etc resentment against the Umayyads made them popular and the transition was not fractious for the Umayyad empire with the exception of Spain. The Abbasids were not as intolerant as their Umayyad forebearers either and allowed for the empire to become cosmopolitan. The inclusion of non-arab peoples into government helped administration of the empire and quell unrest. For instance, the Abbasids moved the capital of the Empire from Damascus to Baghdad (in the old Sassanid empire) and Persian culture was once again celebrated. Islam was no longer viewed as a religion of the Arabs but rather a religion of Arab origin. Non-arabs were no longer forced to feel as second class citizens.