The one-line difference
Mykonos is a beach and nightlife island with a beautiful town; Santorini is a landscape and sunset island with modest beaches. People who want to swim, sail and stay out late choose Mykonos. People who want the caldera view from a terrace choose Santorini. Plenty of people do both in a week.
Beaches
Mykonos wins clearly. Its south coast has a string of sandy, sheltered beaches with clear water, sea taxis between them and every kind of atmosphere from family to party. Santorini's beaches are volcanic — black or red sand and pebbles — and are a drive from the caldera towns; they are interesting rather than idyllic.
Scenery and towns
Santorini wins on drama: the caldera cliff villages of Fira and Oia are among the most striking views in the Mediterranean. Mykonos Town is the prettier place to wander — a flat, whitewashed maze with windmills, Little Venice and working harbour life — but the island's landscape is low, dry and windswept rather than spectacular.
Nightlife and food
Mykonos has the nightlife — beach clubs by day, bars in the lanes until dawn — and a deep restaurant scene from fish tavernas to fine dining. Santorini's evenings revolve around sunset dinners with a view, wine tasting on the volcanic vineyards and quieter bars.
Crowds, wind and cost
Both are expensive and both are crowded in July and August, with cruise ships adding daytime surges. Mykonos has the meltemi wind, which is strong in high summer; Santorini is calmer. Mykonos beach clubs and Santorini caldera hotels are each their island's premium-price trap; both islands have good value if you step one street back from the famous view.
Doing both
Ferries connect the two islands in season, typically in two to three hours on the fast boats, with several sailings a day in summer. A common week is three nights on Mykonos and three on Santorini, or either island paired with Naxos or Paros for a quieter middle stretch.