Personally, I had a much better time on Ibiza than I did on Mykonos. While I visited both islands during peak season, Ibiza felt much more able to handle the massive influx of tourists, while Mykonos just felt ... crowded.
Beaches, clubs, roads, and tourist attractions felt overrun in Mykonos. I'm sure if I visited the island a decade or two ago, I would've come back singing the praises of a magical Greek island, but today, the island feels ill-equipped to handle the sheer number of people that want to vacation on the 33-square-mile island.
In Ibiza, I had a number of excellent budget lodging options to choose from, deserted beaches along the coast to lounge on, an entire countryside to explore, and zero trouble booking tickets at even the hottest nightlife events of the week.
Mykonos had more naturally stunning beaches with possibly the bluest waters I've ever seen and the day parties on the beach were much more hip than Ibiza's. But, at the end of the day, most of the parties felt like a scene. You were either wealthy or beautiful or you were nobody.
It may be because Ibiza is a party hotspot for young Spaniards as well as the vacation set, but Ibiza's clubs felt accessible and welcoming.
I think it comes down to money. Because Mykonos is so crowded and expensive, it really only makes sense if you are a millionaire, billionaire, or someone wanting to feel like one for a week (savings account be damned).
It sounds weird to say but for most people, from backpackers to families to couples on honeymoon, I'd recommend Ibiza as the island to see.