Marik's Knights were meant to be symbols first and warriors second, whereas Stone's Knights are the other way around. Both are meant to be an ideal that other soldiers(and the citizenry) could aspire to and hopefully emulate, and also provide the state with a small force of elite warriors that can be called upon in times of need.
I think a lot of it has to do with the leaders that founded them. I'm going to take a wild guess and say that whoever Stone is, his birth and early childhood would have been in the years of relative peace after the Fourth Succession War, while his teens would have seen the arrival of the Clans. On the other hand, Thomas Marik's formative years were in the depths of the Third Succession War. Both knew war from an early age, but when Marik was forming his worldviews, there was real concern that humanity was in the midst of a decline that might truly be irreversible and that the end of spacefaring civilization as we knew it wasn't all that far off. I believe he wanted his Knights to be a force against that entropy, to prove that humanity could aspire to more than just scavenging among the wastelands of our past glories.
Honestly, the thing I respect the most about the Knights of the Inner Sphere is that despite being primarily a cultural unit vs a military one, they never became a true parade unit. Sure, their mechs were all shiny and new and even the sticks up their butts were recovered tech plated in gold, but when the time came to throw down, they retained the skills to cash the checks their attitudes wrote.
