Pros: Aside from any other differences, Himalayan salt has a more delicate flavor that I prefer over other sea salts. Sea salts and Himalayan salt both have better mineral content than table salt.
Table salt is to rock salt what table sugar is to unfiltered raw cane sugar juice or white bread is to a stalk of wheat. They are emphatically not the same. Did you know that you can make water in a lab that is chemically identical to "real" water (both are H2O), but if you put fish in this synthetic water, they will die? Just because all salt is NaCl doesn't mean they are the same - chemical identity is just one way of looking at something. My hand is probably chemically identical to my foot but it'd be crazy to say that that makes them the same thing because we use more than one measure when we want to understand something.
I don't suggest that natural is always better than synthetic. It's good to research the difference for any given thing - synthetic vitamin C is in no way inferior to natural vitamin C, but synthetic vitamin E carries a serious risk of toxicity that natural vitamin E does not.
However, in a situation where you don't have any research to go on, it does make a good rule of thumb that the natural version is probably a healthier bet. Biological processes tend to require many "ingredients," and natural products tend to leave the entire "package" of co-nutrients intact, making it more likely that you're supplying your body with all the ingredients it needs to do a particular job, and not just the biggest/main ones. For instance, calcium can't be absorbed by the body without adequate amounts of magnesium, vitamin D, and saturated fat present in the body. Whole milk, a natural source of calcium, is also rich in magnesium, vitamin D, and saturated fat. You'll find dozens of other examples like this. (It's no coincidence - natural selection is more or less responsible for this tendency of nature to package nutrients efficiently for our purpose, since animals and our ancestors who thrived on whole foods were the evolutionary successes who got to pass down their genes during the millions of years whole foods were the only foods available on the planet.)