the “son” is related to the boat in which the sailors are.
Both forms are correct but the “son” version put a slight emphasis that the boat might be important. For example the boat has been named earlier in the sentence.

The meaning is essentially the same, but there are sentences where you’re forced to used one or the other.

Tout l’équipage est à bord.

You didn’t mention the boat so you can’t use “son“

Le sous-marin compte 25 personnes à son bord

You’re talking about the submarine’s crew, so “son” is needed to indicate the genitive case.