The water issue is independent of whether the farm is vertical or not. There are plenty of hydroponic farms that are in a traditional horizontal orientation, I presume aeroponics can be setup this way as well. So, I do think the smaller area is the main advantage, though I'm not convinced it is a compelling enough reason given the increased energy, land and capital costs.

I agree that water should be treated as more valuable and scarce than it currently is. You mentioned the Middle East, I saw this concept for a "seawater greenhouse" recently in Qatar and was intrigued

http://www.sciencemag.org/news/2013/11/desert-farming-experi...

In the US, I'm curious about the scalability of these water saving technologies. Could they replace a significant percentage of vegetable production of drought stricken California? As I understand it now, hydroponics is used primarily for winter production, even that competes with Colorado River dependent Arizona.