Recently I have heard both of these variants in the news with reference to the missing Argentinian submarine:
....avec 44 marins à bord.
....avec 44 marins à son bord.
Is there a difference?
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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.