Does the GL2 and the XL2 have the same image stablilizer? The XL2 looked pretty good in that demo video. I don't beleive my GL2 is that good.

The image stabilizers are in the lens assemblies, not in the camera/recorder assembly.

Yes, to my knowledge the GL2's IS system is fundamentally the same as the XL2's standard lens, although the latter may have introduced some refinements. Canon's optical IS system is arguably the best in digital photography.

But you're not comparing apples to apples if you're comparing your handheld GL2 footage to the XL2's demo.