Stephen has lost his ability to do Hand Signal spells due to WWH braking them. He lost his teleportation spell on a universal scale recently as well meaning no one can use it EVER!
He is pretty much limited to voice activated spells and Astral manipulation which requires his physical body to remain vulnerable.
Zatanna's cheap voice activation spells would be too much for present Strange.
Seven Soldier's Zee was powerless, though. She had the New God artifact with her, hardly fair.
And yeah, as everyone says...current Dr. Strange would lose, classic Strange would win. Zee is often too much of a plot device, but it's clear that when she comes up against the real heavy mystic heavy weights in DC (Arion, Dr. Fate) she is overmatched. Dr. Strange is on that level
Zatanna has been portrayed in the leagues of Dr. Fate and the like for years now, and magic is basically the most potent plot device in comics so I hardly see her being more of plot device than any other magic user.
To the best of my knowledge, no she hasn't. Dr. Fate, Arion and Mordru are legitimate Lords of Order and Chaos, cosmic beings taken human form.
Zatanna is from a magical race, yeah, and her powers often times seem to be Deux Ex Machina, but only until she comes up against other actual sorcerers. She was talking about Arion like he was the scariest mofo around, and he would have been Dr. Fate level.
Magic is a plot device, yes, but Zatanna is sort of the pinnacle of that. She gets taken out by Deathstroke or the Joker, but only has to utter "pots" to defeat the JLA-owning Despero and the Injustice Gang.