The updraft idea (as outlined in the Popular Science magazine) makes more sense to me, as there you not only can use natural drafts created by wind, but as is stated you can use waste and/or solar heat to create additional draft to even out variations in natural draft. In the downdraft version, the power you generate is based on the weight difference between dry air and moist air, and it seems like you'd need a lot of air.
At least part of the draw selling green energy to California's Global Warming Crisis™ was that instead of adding waste heat or solar heat to increase power, the evap tower was going to use the already existing solar heat in the atmosphere, generate power, and spit nice cool air out the bottom.
It does need air and large scale for the tower, but figure they are pumping water to the top and dropping it down the tower. Almost all of that water (in terms of weight, not as water) is going to down to spin the turbine. It is A LOT of air, and even a lot of water.
That article linked used the figure 8,000 acre-feet a year, which is a little more than the amount 16,000 homes use in a year. It's a lot. Probably has an allowance for waste/loss in storage and transportation, but we're going to use it for rough numbers. So divide that by 365 days a year, you get about 22 acres feet a day-- here the real figure for days is probably lower, because you're going to have factor downtime for maintenance and weeks of cold, moist weather, but again, it's the only numbers we're given, so we're rolling with it.
(Reasonable assumptions are: A little less water getting to the top of the tower, and less than 365 days a year operating. We can ass-u-me they wash and do some stupid math just to get an idea of the massive amounts of water planned for the tower....)
Using the numbers above, if it operates 14 hours a day during the hottest parts of the day, using 22 acre-feet, that's over 500,000 gallons an hour. Over 8500 gallons per minute sprayed, evaporating, adding it's weight to the air, at over eight lbs a gallon, that's somewhere close to 70,000 lbs added in a minute -- which then accelerates down the tower via gravity.
So it's massively scaled for a reason. It's not just that the damp, cold air weighs more than hot, dry air, it is also accelerating down the tower from where the water was added up towards the top.
Having said all that, how efficient the capture is depends on the outside weather. Otherwise you're just sending liquid water down, and that's a losing proposition.
Again, building a simple green house, with or without mirrors at the base of a tower and using the
updraft seems a lot simpler, uses no water in the desert, doesn't require lots of large pumps or as large a structure, little or no maintenance apart from the sole moving parts (turbines), etc.
But the down draft tower is a fun marvel in it's own right. If it ever eventually exists.