If you are short on time, here is the decision in one paragraph. The Şehir Hatları public ferry (the official Istanbul ferry company) is cheap — approximately €3–5 per person depending on route — and gives you a long, unhurried ride up the full length of the Bosphorus to the village of Anadolu Kavağı. But it takes about 6 hours round trip, has no food service beyond a basic canteen, no English commentary, and no reserved seating.
A MerrySails Bosphorus cruise gives you the scenic highlights — the palaces, mosques, fortresses, and bridges — in 1.5 to 3.5 hours depending on the cruise type, with drinks, food, entertainment, and professional commentary included. The sightseeing cruise at €15 is the closest comparison to the ferry experience but in a fraction of the time. The sunset cruise starts from €34, and the dinner cruise now runs on a €30 to €90 package ladder depending on seating and drinks.
The right choice depends on your budget, available time, and what kind of experience you want.

