the Islamic world, around 950 AD, the most sophisticated civilization

I wouldn't say that the Islamic world was definitively the most sophisticated civilization in Europe and the Near East. Again, as I often like to point out, you are missing another very important (and equally sophisticated!) civilization that lay between Western Europe and the Islamic world - that of Byzantium. The Byzantine Empire was at worst, an equal of the Islamic states in sophistication, and at best, their superior. I could go into a lengthy discussion on this, but I'll save that for another time.

Anyways, I would argue that Western Europe could certainly have been considered a civilization in its own right. There were many powerful, centralized kingdoms that were beginning their rise to prominence in AD 950, notably, Capetian France (officially established by the late 10th Century) and the German Holy Roman Empire (which would be founded just 12 years later by Otto I in AD 962). The Spanish Kingdoms also rose to prominence during this period, and solidified their position against the Moors, allowing them to initiate their long Reconquista. Even England had been essentially unified since the early 10th Century. All of these kingdoms shared a common religion (Roman Catholicism), a similar cultural legacy (most being descendants of both Romans and certain barbarian "invaders"), a common language (Latin, which remained a universal language of learning), and an agricultural-based economic system with a strong feudal hierarchy.

For centuries prior, the Merovingians and the Carolingians ruled as Kings and Emperors over vast swaths of Western Europe, which generally prospered under their leadership. Literature, law, architecture, and art flourished during what is known as the Carolingian Renaissance of the 9th Century. There were also many writers of the West who wrote outside of this period, exhibiting wide-ranging intellect and a love of learning. Renewed relations with the Byzantines around the turn of the 10th Century allowed Western Europe access to many exotic goods, ancient manuscripts, and new technologies, which helped to begin the rise of the West in the centuries that followed. An increase of trade in the Italian maritime states with Byzantium and the Islamic world also helped to further the development of the West's economy, which would eventually overtake the Byzantine economy in the 13th Century.