tl;dr: Cruise emissions are lower than flight emissions even before switching to LNG, which might have unintended consequences due to leaks in the supply infrastructure.
Carnival Cruise Line published an independently verified sustainability performance summary in 2018. According to this report, their ships release 251 grams CO2e per ALB-km. ALB-km is a measure like passenger-kilometer (pax-km), but in this case refers to "available lower berth" (source), which typically has capacity for two passengers.
If we generously assume a 20% improvement from the switch to LNG, emissions would drop to 200 g CO2e/ALB-km, or 100 g CO2e/pax-km.
Emissions for air travel is more complicated, because it depends on the distance and type of aircraft, among other factors. There are at least two different calculators that take these factors into account.
- The ICAO carbon emissions calculator from the United Nations International Civil Aviation Organization.
- The flight emissions calculator from the myClimate Foundation, a Swiss non-profit. In contrast to the ICAO, this calculator includes an estimate of the non-CO2 impacts of flying, such as high-altitude NOx and contrails. The specific impact of these effects is still being worked out, but this calculator includes a conservative estimate.
Cozumel, Mexico, is a popular Caribbean cruise destination. There are also regularly scheduled direct flights from Miami, USA, so it makes for a good comparison. It's a round trip flight of 1,792 km.
- ICAO calculator: 266 kg CO2, or 148 g CO2/pax-km
- myClimate calculator: 0.400 mt CO2e, or 222 g CO2e/pax-km
At 126 g CO2e/pax-km, a conventional cruise ship is already better than the lower estimate of 148 g for flying, and has about half the impact of the higher estimate of 222 g. Thus, any improvement in cruise ship efficiency from a switch to LNG, while welcome, is superfluous -- it was already better than flying.
Leaks in natural gas infrastructure
But there's a catch -- recent studies indicate leaks in natural gas infrastructure have been underestimated for years, and methane (the chief component of natural gas) as a greenhouse gas is 34 times more potent than CO2 on a 100-year timescale.
So switching from diesel to LNG (which is made from natural gas) might actually be worse from a life-cycle emissions perspective.