I'm going to jump in a bit late on this one, because I came across the DMX Airflow this weekend at Home Depot, and I have to look into it some more, but so far it seems to be the most promising underlayment for my basement.
Now, a few things... DMX produces several types of underlayment.
"DMX 1-Step" is from what I can tell, a more traditional dimpled plastic underlayment, where the dimples are pushed out on the bottom, leaving concave dents on the top. It seems to have a top layer of "closed cell waterproof foam" and has a stated compressive strength of 6,000 lbs/ft2. Dimple height is stated at 8mm.
"DMX Airflow", which is the one I saw this weekend, is a bit different. It has a solid flat foam top layer without the concave dents, and seemingly solid foam protrusions on the bottom. They look like coins, basically. It says that both sides are "closed cell waterproof foam" and it carries a stated 8,250 lbs/ft2 compressive strength. One of the product videos I saw states that it has a "high impact plastic" encapsulated between the foam layers (this layer contains the 4mm dimples, and is then sandwiched between 2 layers of foam). I wish I had measured the total product height, I may have to go back and do that.
What I like about the Airflow is that it provides a little insulation (stated R 1.2 value), it has a soft foam layer on both sides, which should reduce or eliminate clicking sounds, and it is thin, which means I won't have to give up much height, which was one of my main goals in this basement project. Our floor is going to be 12mm laminate. It should provide some give (at least more than the concrete would) when the kids inevitably fall on it, and it seemed pretty durable. We don't have moisture problems in the basement, and I'm not expecting this to save us from any floods. I'm going to do some reading, but there isn't a ton of info about this stuff online. Bottom line is that to me it still looks better than the usual suggestions, being that junky red plastic that looks like it has tiny styrofoam balls glued to it, or solid cork which wouldn't breathe at all (just in case).
Here is a quick comparison I made from their product photos, and a few I snapped from in the store. And the styrofoam/thin plastic sheet alternative.