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).
Well, that's a bold claim, but let's see if Photoshop really is inefficient. I took the original iguana image from the Compressor site, and then used Photoshop save for web to bring it down to 250kb (same size as the after image from Compressor).
I picked a spot and zoomed in where it's easiest to see the artifacts.
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.