In usage, their ults should be functionally similar because that's what they're said to do - to move people towards a location to set up for something, whether it be Shyvana's Q/W/E aoe or Azir's W -> Q soldier spam.
In reality, Shyvana's ult does almost nothing, half the time can be a detriment even though it has comparable base damage, and it's only good if she lands right on top of people in order to try and multi-Q. Azir's ult is always functional, does a lot more utility, has much lower risk as they can't immediately turn back upon you without using an actual blink (not a dash) or Flash to get over, and sets up for his team much better.
Azir does absurd amounts of damage come late game, as well as a playmaker. Shyvana just tanks it up and does moderate damage late game. In the midgame, they both do absurd damage but Azir's still a playmaker. If he can do this from range and with minimal turn potential if done correctly, why can't Shyvana get some consistency in her ult pull distance?
Shy's ult is glitchier than Azir's entire character was on release, and if they just fixed the god damned hitbox on her ult to be accurate and not wonky as hell she'd be fine. That's all that's really needed to push her in the correct direction with it.
edit: i understand she's strong i swear to god if you people strawman that into this discussion i will literally take a fork and stab your internet wires with it