I've both cameras right now and they are almost different machines which happen to take pics.
The 5D3 is overall slightly more responsive in AF, card writing to clear buffer and fps among other things. The 16-35 f2.8 II is slightly sharper in the corners than the Nikkor version, plus it's f2.8 so it focuses better in lower light.
As Fred said, no flash on the 5D3 means the camera is also slightly more compact and so the housing is smaller and lighter as well. I like the fact that most of the essential controls can be actuated from the Q (INFO) menu, which is very beneficial to quickly changing parameters from metering to drive modes. I use it that way more often than the viewfinder. The 5D3 have fewer buttons for controls, relying on menus UI. I personally like this vs the plethora of buttons and dials on the D800.
For instance, the metering control is a small dial which is a pain to actuate topside. On a housing, for eg. Nauticam, it's a big dial on top so one has to lift the right hand to change modes. Then again, how often do you have to change metering modes?
It's really nitpicking but that's the point of getting the pros and cons. One usually gets accustomed to these features and just work through it.
As Whitey says, the Nikon D800 is all about the sensor. The dynamic range from 100-400ISO is very wide. The ability to pull details from shadows and highlights in the 14bit RAW files is very impressive. The difference is visually noticeable, although it's not glaring, but still impressive. In most circumstances, the difference will be negligible, but those high contrast scenes will benefit a bit,especially in post. That's the main reason I'm evaluating the D800 with housing. 36mp is also nice to have to crop.
One more thing is the memory cards. With the 5D3, the CF slot is much faster than the SDHC slot. It's like the SDHC slot has a speed limit of 20MB/s, handicapping the 95MB/s cards. Hopefully they'll get a firmware upgrade to fix that. The CF card flies though, forcing me to upgrade my cards to squeeze the fps. The D800 SDHC slot is noticeably faster with the fastest cards.
I'm not sure which part of Ireland you're in but Loftus' suggestion on going out to test the cameras is a good one. That's probably the best way to evaluate the cameras.