The 14 to 24 mm Nikon zoom lens on the 35 mm (FX) sensor has an angle of view of 114 degrees at 14 mm, the Olympus 7 to 14 mm zoom lens at 7 mm has an angle of view of 114 degrees. Given the same shooting situation the images would be all but identical. Since the Olympus lens is 7 mm at 114 degrees and the Nikon 14 to 24 is 14 mm at 114 degrees the Olympus has greater depth of field using the same F/number on both lenses.
Yes but you don't shoot different formats at the same f-numbers. Stop the 35mm lens down 2 more stops and the DOF is the same and so is the theoretical resolving power. The 35mm system will offer the possibility of higher resolution and/or better dynamic range by virtue of a 4x increase in light gathering capability. It will be preferable for sunballs. The bigger the sensor the better as long as you have enough light.
As Alex Mustard has said several times given the dome port for underwater use the smaller sensor sizes seem to have several upsides over the larger sensor sizes, thats is one of the main reasons we didn't use medium format film cameras for U/W photography because of the narrow depth of field for the wide lenses and that at life size (1:1) with macro lenses the image size was 6 X 7 at 1:1, over four time the 35 mm size.
I disagree with both of those points. MF is a higher resolution format so that's why it's DOF is perceived differently. The real reason for not using it underwater is lack of suitable optics for both wide angle and macro. As for dome ports, they are format-agnostic. Dome ports are about resolution and angle of view, not format size. That Subal dome for the 14-24 may also help the Sigma 10-20.
I think the important point Alex made is that IQ at base ISO between Nikon FX and DX is difficult to differentiate. Given that, it's hard to argue in favor of FX and the 14-24 when you can use DX and a 11-16 or 10-20, particularly when you can use diopters with the DX lenses and you can use the 10-17 as well. Until FX gets bumped to 20+MP on the Nikon side, there isn't much to recommend it underwater. Above water, I'd rather have FX even at 12MP for the same reasons Paul likes it.
It all boils down to the specific cameras, the specific lenses, and the specific ports and what gives you the most of what you want. Right now on the Nikon side, there isn't enough with FX to make it compelling for most people. A zoom fisheye, better domes, and 20+MP will fix that.