My vote would go with Synthetic, not by far, but just a bit. But as per usual its the why that I find more interesting.........
Lets think about it.
The first thing to start dying back when ca, alk and mg becomes depleted, will be corraline. This will happen before any corals start showing signs of ill health. Another very important factor in corraline growth is the ratio of ca, alk and Mg. Here nsw gets a bit ahead, as often synthetic mixes do not match nws ratios perfectly. (And Jah knows best mon!) However, the ratio of these three important factors rapidly become skewed in nsw, as acidifying processes rapidly consume the buffering reserve, i.e. what we measure as alkalinity. Synthetic mixes have a higher buffering capacity for alkalinity, so they are able to maintain the ratio of carbonates, Mg and Ca for a longer period of time.
We can get a lot more technical, and bring a calcium reactor into the mix, but i suspect that even then synthetic will win. Unless of course the reactor media releases more carbonates (in a ratio at which acidifying processes deplete alk) You see where I am going?
Not taking anything away from your interest in starting a debate we can all learn from, but, Does it really matter.
Whether you are using nsw or synthetic, just keep the ratios correct, the levels in check and stable and corraline will follow.
If you want to find out the truth, do you suspect someone told you an untruth...... Maybe as a sales pitch, guessing for synthetic??????? If that be the case, they need to rethink their strategy, (go back to salesman school) as the difference in a well maintained system with either nsw or synthetic would be small enough to be called insignificant.