Do they armor types affect what upgrades are available for the unit. IIRC correctly, the armor factory provides "advanced plate" -- does this mean that Lancers are actually a unit that can benefit from the amor factory?

What I'm really looking for here, is anyone who can tell me if there is a practical difference on the battlefield between these 3 types of knights. Is there any reason to work up to Chivalric Knights or Lancers when French Nobles are already available?