Both diving gear and neptune's shell provide the ability to breathe underwater and swim in water. Diving gear also works with lava, though continued exposure to magma without obsidianskin potions is going to result in timely demise. Yet the wiki claims Neptune's shell is better in unspecified ways. What should one consider when choosing one over the other?
Using the diving gear actually only doubles your lung capacity, it doesn't allow you to breath under water, which Neptune's shell allows you to do.
Not only that, but you lose 0 speed under water while you're using Neptune's shell, it's exactly like you are on dry land (except that you can jump infinitely).
Pretty much, while you still have to worry about water with the diving gear (just less so than normal), with the Neptune's shell, all water becomes like air anyway, you can just ignore it.