I would take the creature on the helmet from Paris to be a bird of prey, something that would be a natural type of creature to be associated with the god of war: ample literature exists to describe birds eating the corpses of the slain after a battle, and a raptor has its own fierce persona as something that hunts and kills.

It's more difficult to understand what the artist from the Meyer source may have been considering. This is clearly a dragon, but since it is one artist's vision and we don't know the artist or what he might have been thinking, it is not possible to discuss why he is associating a dragon with Mars. This sort of dragon would not have been part of the iconography of the ancient Mediterranean, where large serpents - often sea-going - were the way dragon-like monsters usually manifested. But for a modern artist, it isn't a huge leap to place a demonic, winged agent of destruction on the helmet of the god of war. How that artist made that leap, however, is anyone's guess.

Just to be sure: you're aware those are baroque depictions?