I disagree.OP lots of really good feedback from people that really do know cave diving . BUT noone has actually answered the question.
Taking all the other stuff they are talking about out of the story then NO there isn't any difference between being in a cave at 20m (60 feet) or being out in the open ocean. Pressure is pressure/depth is depth.
If I am, for example, at 130 ft in open water on air or nitrox and I feel impairment by narcosis coming on, I can ascend, 10,20, 30 ft until I am comfortable. If on the other hand I am at 130 ft in a cave on air or nitrox, the options for immediately going up are much more limited, and "up" may be several hundred feet back or farther along the cave passage.
Another issue is that visibility tends to be more constant in OW. Even if an area is silted out, it is generally limited either horizontally or in depth. And even if the whole ocean suddenly goes low viz/zero viz, I can still ascend to a shallower depth/lower END and then swim a compass heading without the effects of narcosis. In contrast, if the viz goes to zero in a cave, it can last for hours and impact the entire egress from the cave. Thus I now have to navigate on the line in low/zero viz, potentially for hundreds or thousands of feet at an same END that while ok in good viz, is now problematic in no viz.
The ability to not be able to immediately reduce END is a big difference, even if the water depth and pressure are the same in OW or in a cave.