Both positions are defensible. An undocumented position is not, and that is the part inspections turn on.
What Each Gives You
Liquid phase holds samples immersed. Temperature is most stable, the gradient through a canister is negligible, and hold time during a power failure is longest. Vapour phase holds samples above the liquid, removing contact with the nitrogen. The ASRM and SART Practice Committees, writing on cryostorage in Fertility and Sterility (2020;114:486-491), note that liquid nitrogen is not sterile, which is the basis of the vapour phase case.
What Each Costs You
Vapour phase introduces a gradient up the vessel, so the top of a canister sits warmer than the bottom. That matters because the damage band is not room temperature but roughly minus 130 to minus 80 degrees, where motion has resumed while the sample still looks frozen. It also leaves less tolerance if level falls, which is why the same committees recommend level probes in the liquid over temperature probes in the vapour.
Either choice is defensible. An inherited one is not. Vessel options across both approaches are in the storage vessels range.