It depends on your preferred play style. Illaoi and Ivern are both very different from each other, and they have vastly different roles in a team. If you're flexible enough not to care about that, then really, it's about preference. Illaoi is a very aggressive top-laner, and as a juggernaut, she's kind of slow, but hits very hard. Her tentacles do take a bit to get used to, but they're not too difficult to understand in practice. They spawn passively, and the best time for you to be aggressive is when there's a bunch of them up. Her W will bring all of her close tentacles down on the enemy, so it's a great way to deal a lot of damage all at once. Plus, if you have a bunch of tentacles up before you use your ult, then that's even more damage because your ult spawns more AND makes all of them smash down. Illaoi's great in team fights because of this.
As for Ivern, he's a jungler, but his passive means that you don't actually have to fight the jungle camps. Just click on them and wait for that little green circle to fill in with light (or just use Smite) and you'll get all the gold and experience from that camp. Pretty neat, especially in practice! He's a great counter-jungler because of this, as he doesn't have to actually fight the other jungler. Ivern is a lot more passive in his play style as a jungle-support character, aiming more to aid his allies than actually kill enemies. He's excellent at setting up enemy laners to be killed by his teammates, and he's capable of holding his own once he has his ult. But don't really expect to carry with Ivern - he's not really fitted to be too much of a damage threat, but his utility is top notch. You'll want to gank a lot with him.
Of the two, I feel Illaoi is easier to learn, but Ivern could have a bigger impact on the game, depending on how you play them. Really, the choice is yours. ^^
