I've installed DriCore in my basement. I won't know how it sounds for another month yet and won't be able to compare much to Acoustic Mat.
What I can tell you is that DriCore is incredibly easy to install and it adds a great deal of warmth (my secondary reason for installing it) in my basement. Stepping in bare feet from DriCore to bare concrete is quite a shock.
The only thing to keep in mind is local building codes and if the addition of either will offset any rise between floor level and any steps/stairs leading to that level. Code in Wisconsin restricts variences between steps to less than 3/16". I only had to modify two steps between the floor and a transitional platform and was able to do so by a bit of measuring, some trial and error and a friend with a nice 13" planar.
If you are in the Wisconsin area, you are welcome to come over and listen/feel for yourself in a month or so, once my home theater is completed.