Mykonos is about the energy. It's louder, younger, and more international than Santorini. The famous windmills and Little Venice make for great photos, but what Mykonos is really known for is the beach clubs, the late nights, and the party that runs from June through September without stopping. It's also increasingly a luxury destination — the high-end hotels and restaurants here are some of the most expensive in Greece.
In short: if you want scenery and romance, choose Santorini. If you want beach life, nightlife, and the full summer Mediterranean experience, choose Mykonos. If possible, spend two or three days on each.