I'll narrow down a bit in this follow up, were we looking at the same kind of fighting style?

Alexanders phalanx and the Christian men at arms break the enemy charge while the cavalry wheels around behind to cause carnage?

I guess the next question would be how the Persian/Roman Cataphracti would compare in this wise.

A follow up question, I've often heard that something like a cataphract and knight were very similar in their role on the battleflield but they were different because the knight was actually a social rank while a cataphract didn't have to be a noble or lord.

What about companions? I understand their role on the field was different Companions being a flanking force, but did their role as "Companions" carry over in every day life? Was it actually a social rank?