Ideally, you would get both Aperture and Ps Elements..... though I know that may more money than you want to spend. However, they do different things.
Aperture is a Digital Asset Manager, that helps you organize and collect your images... and it also does some editing. Edits done in Aperture are 'non-destructive'. Also, you can create many versions of a an image in Aperture with no space penalties.
Ps E is an editing application. It edits by replacing the original with the edited version (by default, though you can do a 'save as' - if you remember). Different versions take up more space. However, the editing capabilities of Ps E are greater than what you can do with Aperture.
Generally speaking, most photographers will do their organizing Aperture and the bulk of their editing. They will then use Aperture to send some images to an editing application, such as Ps E, for some heavy duty editing. The editing program returns the finished image to Aperture which stores it next to the original master image. This is one of the few instances where different versions of an image in Aperture actually do take up extra space.
Hope this helps....
