In the literal sense of the word “to mark”, the difference is obvious:
something is marked with markings (= symbols, added visuals)
by the painter(s) (= the person or persons who made the markings).
Passive voice: The stone is marked with hieroglyphs by unknown ancient Egyptian carvers.
Active voice: Unknown ancient Egyptian carvers marked the stone with hieroglyphs.
So what if one uses “to mark” in a metaphorical sense?
I would use by when the thing that follows is the trigger: an emotion, such as scorn, that drives a person to behave differently than he otherwise would.
The politician’s speech was marked by scorn for the rival party.
= The politician or his speechwriter had so much scorn that they just couldn’t write a speech in which the rival party was refered to in a polite, respectable tone.
Scorn is here the driving force.
I would use with when the thing that follows is something that can be seen, heard, or sensed: not the driver of the markings, but the way the markings are visible, audible, or sensible.
The politician’s speech was marked with scorn for the rival party.
= You can just hear the scorn in the words of the speech.
Scorn is here the output. The politician’s speech was full of scorn for the rival party.