Taking the Iona as an example, it is claimed that

"The cruise ship will have a reduced carbon footprint with zero sulphur and nitrogen emissions."

Sulphur and nitrogen, while pollutants, are not greenhouse gases, and I'm asking specifically about the impact on the broader climate.

This article argues that flying is "three times greener than cruising".

Carnival claim LNG offers a 25% reduction in CO2

However, this article discusses the benefits of LNG in shipping and seems to suggest the greenhouse gas emissions of LNG are only 6% lower than heavy fuel oil on average.

My interpretation is that the benefits of LNG are only slight (from a climate perspective) and therefore flying is still lower impact than cruising. But I don't know if these claims are on a like-for-like basis.

Are there any studies that do a direct comparison of modern aircraft to modern LNG-powered ships?

N.B. I'm aware it is hard to compare the end-to-end climate impact of a holiday, considering the cruise ship has features and services built-in, which would be provided separately by a destination that you fly to (and therefore not included in the emission cost of flying).