Photoshop export (yes, even Save for Web) is notoriously inefficient. As others have mentioned here, ImageOptim (and the various command line tools it uses) can make your images significantly smaller (particularly PNGs).
I picked a spot and zoomed in where it's easiest to see the artifacts.
http://i.imgur.com/Sf72oZq.png
If anything, I'd say the Photoshop one is better than Compressor.