Compare like with like before paying
Put both complete offers beside each other. Match the actual time aboard, the activity, return transport and the number of people travelling. Then add the costs that would otherwise sit outside the headline price. For a private quote, divide by the guests who are actually going; an empty place aboard does not reduce your group's real spend. For a shared tour, include child fare rules and any separate transport your party would need.
The question is what you receive for the difference. A couple might choose the social atmosphere of a shared excursion. A family with a particular pace, or friends celebrating together, might put more value on having the boat to themselves. Neither choice needs to be justified as the most luxurious option. Choose the format you would enjoy during the ordinary moments between the photographs.
Before committing, read the cancellation and weather terms for that booking and confirm how a changed cruise itinerary would be handled. Private does not mean every request can be accommodated, and a shared ticket does not automatically include the transfer you need. Send the same trip details to each provider so the comparison stays fair.