I think Azir will be the same after the mage update. He's more mobile and his displacement is easier to work around because it pushes people in a direction, so you have a general idea of where that person will go, where Zyra's just knocks them up, and she is fairly immobile comparative to Azir. Azir's soldiers also don't die, so it's harder to escape them where Zyra's plants are killable.
Azir also offers more control in the form of a turret and the threat of his soldiers being able to go anywhere anytime, where Zyra is forced to put her plants near her (I will admit she is able to put more down at once with her update, but that is at the mercy of her passive and W).
Azir also has way more attack speed, so it's easier for Azir to help push towers after he gets Nashor's, max W, and even using his W on turrets to add more damage.
Azir just has a different niche and is not as easily accessible as other mages. But that's fine, I'm patient enough to learn the techniques of Azir and learn around those. The mage update will add some other build paths with the new items, which I am excited about.
Zyra will be more of a control mage, Azir will be a little control, but mostly about huge DPS, similar to a marksman. It's a good niche to put him in, there are a few ADC's who aren't about super DPS.
And if I need a break from Azir, I can play new Vlad. He's looking more fun compared to the current Vlad.