This isn't exactly an answer to your question, but it's a commentary that gives some insight in the matter and maybe could serve to someone else with more knowledge to develop further:

In the books 'A history of Warfare' and 'Carnage and Culture' by John Keegan and Victor Hanson respectively, the authors argue that the west, beginning with Ancient Greek hoplites, developed a preference for decisive warfare, also called shock warfare, in which the the purposes of armies was to clash and engage in hand-to-hand combat, without any kind of delay or indirect tactics.

They argue this was a singular development that almost didn't happen anywhere because it goes against the inherent sense of self preservation from human nature. Almost all other armies prefer to fight in skirmishes, hit and run tactics, attacking supply lines, etc. Not in decisive, hand-to-hand combat.

So, going to the period you're talking about. The authors say the Knights of medieval Europe are a evolution of the shock infantry of past times (notably greek hoplites, roman legions and the "barbaric" armies that rose from the contact of those tribes with Rome). They are designed for hand-to-hand combat, for direct attack, hence the heavy armor and lances. The Islamic armies however, came from a different tradition, they are light armed because they want to avoid that kind of confrontation. They prefer engagement from a distance or hit and run tactics. Reading those books, I got the impression that the image you're asking if is accurate is indeed that. The two armies had different takes on warfare, and although it's hard to imagine an army composed exclusively by a single type of unity, the bulk of them, especially the part designed to win the battles, were indeed heavy shock cavalry for the europeans and light skirmish units for the eastern armies.

However, I have to say I'm not entirely convinced by that theory. For example, neither authors talk about the heavy cavalry employed by both the Parthians and the Sassanians, the latter which was conquered by the arabs. And they, as I understand, fought like latter medieval knights, even if both armies also employed great numbers of lighter cavalry, notably horse archers. That combination gave Rome a run for its money, and some of the worse defeats in that Empire history came in the hands of that combination. Point is, the Arabs might have used something similar. Which would make the difference between the armies less notable.

As I said, not an answer, but I hope it helps a bit.

Follow up question. How do british fuedal soldiers fall into these descriptions?