Start with the shape of the day you want, because Naxos sells four different shapes.
The island-collection day. Three boats do versions of the same run: out of Agia Anna, down the west coast, then island stops in the Small Cyclades. Both Koufonisia cruises (tour-1 and tour-2) both add the Rina sea cave - a cavern on Iraklia's coast wide enough that boats edge inside and swimmers float at its mouth - and both serve a barbecue with the local wine flowing. Tour-3 swaps the famous Koufonisia for Schinoussa and Iraklia, trades a tourist-cafe stop for a WWII aircraft wreck you snorkel above, and undercuts both on price. If you only take one boat day in the Cyclades, it is probably one of these three: "a day trip from Naxos" to Koufonisia is the single most-booked excursion on the island, and 795 reviews on the flagship say why.
The comfort tier. Two catamarans and a proper sailing yacht. The all-inclusive catamaran is the only listing that collects you at your hotel and hands you a towel, with lunch cooked on board from local products. The Lagoon 450F is the mid-price pick: 45 feet of deck, homemade moussaka at anchor, WiFi for the office refusers. The Jeanneau yacht caps at 9 guests, is strictly 16-plus, and is the closest Naxos gets to a private sail without private money.
The short trips. Two hours or one evening. The Panermos Rina Cave run proves the cave does not need a whole day - it leaves from a palm-lined bay half an hour south of town, swims the cave and a calm bay, pours wine at the end, and has you back on a beach by lunchtime. The sunset sail does the golden-hour swim, then champagne from an on-board cellar while the Portara silhouette goes dark.
The history day. The Delos and Mykonos boat is the odd one out: no swim stops at all. Three hours of ruins on the most sacred island of ancient Greece, then Mykonos Town and its windmills - the cheapest 10-hour ticket on the list and, for many, the best day trip from Naxos for a first Cyclades visit.