We wanted to see if a difference existed, and if so, if it would be noticeable in typical use. So there were three types of salt tested in a blinded experiment: plain salt, saltwater, and salt on eggs. For the plain salt, the subject (Jonathan and I both tried it) closed their eyes and was given a plate of salt by the experimenter to sample. The difference in this trial was huge. Jonathan said the sea salt "tasted like the ocean." I wouldn't describe it that way, but the regular salt tasted cleaner and sharper.
Next we took 1/4 teaspoon of each type of salt and added it to 1/2 cup of water. This part of the experiment was double-blind, as I forgot which type of salt was in which cup. There was a difference again, although one was probably not better than the other, and it was much more subtle than the previous stage.
Finally, we decided that nobody actually eats just plain salt, or drinks saltwater, so we wanted to test it with actual food. Neither of us is very fond of salt on food, but we will eat it on boiled eggs. So we boiled two eggs, planning to cut them in half, sample each half with an unknown (to the eater) type of salt, and rate it. I was going to go first. I instructed Jonathan to put 1/4 teaspoon of salt on each half as that was our smallest measuring spoon.
It turns out 1/4 teaspoon of salt makes an egg entirely inedible. Inexplicably, it was worse and saltier than the plain salt we had tried earlier. So we threw that trial out and decided to eyeball the salt on our second egg, which ended up cut into quarters.
Result: I thought the regular-salted egg tasted saltier than the sea-salted egg. Jonathan thought it was the other way around. I think it's because we weren't actually measuring how much salt we used. Either way, when combined with other food, we didn't think the difference in taste was significant.
And now you know.