What is the difference between high and low density anti-static foam in terms of protection against ESD?
Low-density foam is like styrofoam.  You could compare it to a styrofoam cup or egg carton.  Poking it with some IC legs will leave permanent holes.  If bent, it will leave a permanent crease, though it's usually not quite as stiff as a styrofoam cup that can crack.  If crushed (which it's quite resistant to), it will slowly return to some fraction of its original size.  It's cheap and best for one-time uses, like shipping parts.  Many cheap DIP ICs are shipped in bags with their legs stabbed into high-density foam.

High-density foam is like the padding in your tennis shoes. You might compare it to a carpet pad or even (on the extreme end of the spectrum) neoprene.  Poking it with some IC legs will not leave noticeable holes.  If bent, it will bend and spring back.  If crushed (which can be easily done between your fingers), it will return to its original size almost instantly. It's expensive and best for long-term uses, like temporary storage of parts on a workbench or in a toolbox, or in a storage box for an assembled PCB.  Using it for shipping parts gives your part a high-quality association; many of the more expensive parts I've purchased are mounted in plastic protective containers which surrounds two layers of high-density foam cushioning the part contained within.

With respect to the conductivity of that high-density foam; I wouldn't trust the comments of some random person on the internet.  Techni Tool is a highly respected manufacturer.  Their website claims that this foam has a resistance of 105 Ohms/square and dissipates static in &lt;0.05 seconds.  I'd believe that.  This statistic was probably computed by   a chemical engineer and verified by a test engineer with sophisticated equipment like 5-point surface resistance probes and ESD guns.  When I read that comment from 'Breakout Ranger', I imagine an amateur in his basement with a $12.99 Harbor Freight multimeter poking some foam with the stock probes.  Concerning?  Not at all.