In the first set of videos, the kit is run directly into the sound board and out through the house PA system. We actually wished we had gotten a hook-in to the board, we found out after the show that we could have gotten a soundboard recording of the night. We had my kit, a Roland e-Kit, and an acoustic kit set up on stage, and all three going at the same time for the finale. My Alesis held its own against the acoustic kit. Aside from the rush of playing with two other drummers, I had an amazing sense of pride in my setup!
For the second set, it's running into a Behringer XR-18 digital mixer, and out through a Bose PA, which is two speaker "sticks," each paired with a bass cabinet. I believe it's the Bose L1 system (I may be wrong about that). One Bose stick supports a room of up to 200 people. In the outdoor videos, you can see the sticks, one over our keyboardist's left shoulder, and the other unfortunately blocking view of our bass player at times. This is our usual and preferred setup. Most of the places we play require that we bring our own PA, and this one works perfectly. It produces such a clean sound, and in most cases, we don't even need stage monitors, although I usually have one under my kit for an extra boost in sound so I can hear the main mix.
--Shawn.