Hmmm, aren't these 2 completely different programs? Sure, there's some overlap between the 2 programs. I think people typically use Aperture (or Lightroom) to organize their thousands of photos and do *quick* adjustments to their photos.
People typically use Photoshop Elements (or Photoshop) for more detailed work on *individual* photos. You can certainly do post-processing adjustments to your photos using Photoshop Elements, but you can do a whole lot more detailed editing to your photos using Photoshop Elements.
People typically own both Aperture (or Lightroom) and Photoshop Elements (or Photoshop). You typically do a great majority (90-95%?) of your photo organizing and post-processing in Aperture / Lightroom. For a handful of photos that you want to do more work on, you typically use Photoshop or Photoshop Elements.
I'm not sure which one will "outperform" the other, especially since they are such different programs. What performance measure were you looking to compare?