'Better' is always subjective - methane spills from a 1 km long shipping vessel is a lot of potent greenhouse gas back in the air, with an end point issue of using the methane without the C binding and creating CO2 - versus the ammonia with just Nitrogen as waste (or going into ag soils).

Mind you ammonia is an irritating gas and no fun spilled in water at sea .. so, yeah.

The main take home point is that the argument against hydrogen because it's a tiny slippery hard to teansport molecule is a complete furphy - there are other options.

Of course those inefficiencies multiply. You generate hydrogen at 30/40% efficiency. You generate methane from that at a similar efficiency. Then you compress it ... which takes energy. You ship it around. Which takes energy. Then you burn it at 40% efficiency. Numbers rounded up here. Real world efficiencies are worse. Multiply all of that and you end up with efficiencies of a few percent. Nice that it can be done at great cost but there are a lot of things that are probably more efficient and cheaper.