I wouldn't say that Roman authority was completely central under the Emperor. The Emperor was the central figure, but his authority in the provinces was exercised through his governors and the bureaucracy of the empire.
I would also say that during the Middle Ages, it was more common for a king or emperor to try and centralize their authority. Following the fall of the Western Roman Empire, you had various Germanic tribes that invaded and carved their own kingdoms. This split the previously unified provinces being split into small petty kingdoms by the various regional warlords. In mainland Western Europe, you had the Franks who were able to unify the territories of modern day France, Germany, the Netherlands, all the way East to Czechloslovakia.
However Salic inheritance didn't really support centralization of territory, as each son was given territory upon the death of the father. From the 5th century, through the 10th, you had a constant break up and reforming of a unified Frankish kingdom. This process made it difficult to unify. However with Otto I in Germany taking the HRE and Louis taking France, there was a final split of the territory and the rules of succession for both kingdoms were changed. France became a primogeniture succession, starting the centralization of the French kingdom until the French Revolution, by which point the king of France had become an authoritarian.
The centralization of the HRE didn't start until the 14th century. Succession in the HRE was by elective monarchy. When in the 14th century the elective part became just a formality to a primogeniture succession of the Austrian kings, then you had more centralization under the Emperor.
Even in England, there was an increase of centralization throughout the Middle Ages and into the modern era. Following the retreat of the Romans from Britain, there were several successor Britonic kingdoms that were regional. These kingdoms were replaced by the heptarchy following the Anglo Saxon invasions of Britain. Each kingdom in the heptarchy was its own centralized kingdom; however, the kingdoms themselves fought each other in order to obtain supremacy. Following the defeat of invading Vikings, the Anglo-Saxons formed a unified kingdom under Alfred the Great. The Anglo-Saxon Kings held a lot of centralized authority, but the nobility still held a lot of authority as well.
In 1066, the Normans under William invaded England conquering it to add to Normandie in France. William was a ruthless ruler, he striped the Anglo-Saxon mobility of their land and gave it to his Norman allies. This helped to create a central authority in England. This went unchanged until the death of Henry I caused a succession crisis. Following the ascension of Henry II, authority was again centralized under the king. However, during the reign of King John, the nobility were able to force the king of England to sign Magna Carta. This didn't have much effect on the kingdom for some time. But following James I, the strength of the monarch became eroded by the strength of the parliament. This increase in the strength of parliament did not mean that power became decentralized, in fact it was the opposite, the power of parliament and the bureaucracy that formed around it brought more central powers to the British government. But instead of focusing that power on the king, it was focused on the parliament.
In the end, following the Middle Ages, Western Europe was governed by 4 relatively centralized governments, the Kingdom of Spain, the Kingdom of France, the Holy Roman Empire, and the Kingdom of England.