Hydrogen is probably a feasible power source for container ships. Its energy density by unit of mass is very good, though energy density by volume isn't as good as methane. The cost of hydrogen containment is a function of surface area, and containers ships have large fuel tanks.

Cryogenic storage may be feasible for ships, since the ship is surrounded by water which makes heat exchangers work better. Cryogenic storage works by constantly releasing a bit of the fluid to keep temperature down. In the case of a ship crossing the ocean, fuel is constantly being siphoned off to power the boat anyway.

Methane is easier to work with, but the sabatier process (synthetic methane) requires a source of carbon. By comparison, it's feasible for costal nuclear power plants to desalinate water and create hydrogen through thermochemical reaction. The energy used in desalination isn't wasted, since bringing the water up to temperature is the first step in thermochemical hydrogen production.