[Publius Valerius]

It's different in a couple of ways--although I'll begin by noting that I don't think there should be ANY criminal law for speech, and that includes yelling "fire" in a crowded theatre.

But that said, there are some major differences. For one, yelling "fire" in a crowded theatre puts everyone in the theatre in imminent risk of harm from the panic which would ensue as everyone attempted to escape. Notice that it is yelling "fire" in a crowded theatre, not an empty theatre. Falsely yelling "fire" is not inherently punishable--it is only yelling it when there is a serious risk of danger to the public that it is actionable by the state. Burning a flag does not endanger the public in any of the same sort of ways.
Second, there is no inherent political message in yelling "fire" in a crowded theatre, and thus the speech isn't as "valuable" as burning a flag, which carries with it a political message designed to reach an audience to incite political change.

I don't know that I would say yelling "fire" is more akin to action, but there are certainly major differences.

[so_real]

Yelling "Fire!" in a crowded theater may cause bodily harm in the near term. "Citizens" burning an American Flag as part of an I-Hate-America-Political-Statement may also cause bodily harm in the near term if the Flag burner is surrounded by veterans :-) More importantly it may indirectly cause even more public harm as it emboldens enemies foreign and domestic and demoralizes our armed forces. My opinion, but as the apple rots from the core, Flag burning is the more dangerous of the two events.