Hey Smeck,
Good question. For me, the major upside of
Skyclave Apparition is that it's a creature so it can actually kill your opponents. Even if it doesn't have a worthwhile target, it can still get in for damage. Without a worthwhile target, O ring is just a dead card in hand. Additionally, a large upside to Apparition is that whatever it gets rid of stays gone. Chances are whatever you have removed is going to be better than a vanilla illusion.
That said, being a creature makes it fragile, and when it dies it gives your opponent a creature in return. This seems pretty bad against aggressive decks that won't struggle to kill a creature with 2 toughness and will be glad of the extra bodies to attack with.
Oblivion ring is generally much harder to remove so it can do a better job of keeping things gone without the downside, but if it is removed your opponent gets their thing back and sometimes its just dead in your hand.
For me personally, I'd be more inclined to include Apparition. I tend to attack quite aggressively so having a body appeals to me, and I also tend to play with a "make them have it" kind of attitude, so the idea that Apparition dies to removal doesn't bother me as much. The upside when they don't have it is worth it for the downside when they do to me.
I think I'd only really lean in to O ring if I had synergies with enchantments or creature removal was particularly prevalent in the meta. I think Apparition will likely be better slightly more of the time, but it's close. I can definitely see arguments for and against both. Like you say, deck building and meta decisions may well make O ring a much better choice.