If we diverge slightly from the request for CO_2 per passenger km, and look at energy use per passenger km, then David MacKay's book "Without Hot Air" has a rather good chart.
Pulling from that the methods by which one might plausibly cross the atlantic (figures are approximate, as I'm reading them off the vertical scale):
- A Boeing 747: 52 kWh per 100 passenger km (42 if absolutely full)
- An ocean liner: 120kWh per 100 passenger km (102 if full)
- A private jet: 150kWh per 100 passenger km
It's a little unfair to compare a cruise ship to aeroplanes, because the energy used by the ship is not just for propulsion but also the passengers' hotel needs for a number of days - but the majority of it does go into moving the vessel.
So in pure energy terms, out of those options, one must choose the large airliner.
Where do freight ships fit into this? They're not shown on MacKay's chart, presumably because they're not normally a means of transporting passengers. However, one of the reasons that passenger ships burn a lot of fuel is that they go fast - because people want to get places quickly. By contrast, sea freight tends to be carried at something much closer to the most economical speed (and getting ever closer to this, as rising fuel costs prompt shipping lines to introduce "slow steaming"). The very fact that most freight is carried by sea rather than by air suggests that it must be more energy efficient.
In fact MacKay does cover freight transport with another chart, this time in terms of energy use per tonne-km of freight. From this chart,
- Sea: 0.02-0.15 kWh/tonne-km
- Air: 1.65 kWh/tonne-km
Note that this book is some years old, and that the figures for sea freight do not allow for slow steaming; if produced today, it would look even more advantageous for the ships.
It's reasonable to conclude, then, that taking passage on board a freight ship across the atlantic requires at least an order of magnitude less energy than flying - so long as you're not in a hurry!
If thinking about CO_2 rather than energy use, then air travel is further disadvantaged. Jet fuel is a lighter oil than heavy fuel oil, and so probably produces a little less CO_2 per joule of energy provided, but what it does produce is delivered straight into the upper atmosphere, as noted in comments to another answer that link to this paper.
Note also that there are many other aspects that are relevant to just the pollution from these modes of travel, let alone the broader sustainability, such as NO_x, SO_2 and particulate emissions, which vary between transport types.
I don't have the expertise to quantify those effects, but in energy terms the methods of crossing the atlantic from the least energy required to the most are,
- Freight vessel
- Fully laden airliner
- Passenger ship
- Private jet