I have implemented some screens using libGDX that would obviously use the Screen class provided by the libGDX framework. However, the implementation for these s
Black bars on the left/right or top/bottom look better than just distorting your whole scene to fit the screen. If you target an aspect ratio that's in the middle of the possible ranges (4:3 is probably low end, 16:9 is probably high end), then the bars should stay small for most devices. This also let's you use most of the screen even on bigger screens, and you already have that guy's code so it's pretty easy. It would be even nicer if this was just an option built into libgdx.
But, I think the best approach is to use the whole screen. I haven't done this yet, but it will be the approach I take for my next project. The idea is that if someone has a wider screen, then they should see more on the sides. Chris Pruett talks about how to do this in one of his talks (link to spot in talk--actually, the whole thing is actually pretty good). The idea is to scale for height, and then set your viewport wide enough to fit the screen. OpenGL should take care of displaying the rest. The way he does it is here.
For libgdx, maybe there's an easy way to do this with scene2d by moving the camera over the stage, but I've never actually worked with scene2d. In any case, running the app as a native resizable window is a much easier way to test multiple screen sizes than creating a bunch of AVDs.