For most visitors — solo travellers, couples, families, anyone watching their budget — a shared cruise is the right choice. You get the same Blue Lagoon swim, the same Crystal Lagoon cruise, the same Santa Maria sea caves and the same views, for $34–45 per person. Private makes sense when your group is 6 or more people splitting the per-boat cost, when it's a special occasion (proposal, anniversary, birthday), or when you specifically need flexible departure timing.
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The key difference between the two options isn't what you see — both visit the same destinations. It's how you experience it: a shared cruise runs on a fixed schedule with other passengers aboard, while a private charter is your boat, your pace, and your group only. That distinction is worth paying for in specific situations; for a standard first-time Blue Lagoon trip, it usually isn't.