I would consider Elements to be more along the lines of an entry-level Lightroom than a competitor to Photoshop CS5. All three products serve a certain audience, with some overlap between all three as well.

Elements is an excellent entry level tool that allows you to quickly clean up photos at the basic level with prefab tools that do most of the work for you. Some of the things Elements has that Photoshop does not (at least from a built-in feature perspective) are the ability to organize collections of photos, find photos by their content (i.e. facial recognition), and an auto-analyzer that apparently can find your "best work" for you. Elements 8 can also sync your photo libraries across computers.

Photoshop CS5 is, like previous versions of Photoshop, the ultimate photographers tool. Anything that can be done in elements can be done in Photoshop...although sometimes it might require more work and steps to accomplish. Photoshop CS5 offers some intriguing new features that I am dying to try out myself, however, that are not found in any other Adobe product.

The most intriguing feature is content-aware fill, which makes it easy to eliminate undesired elements from your photographs, and fill in the gap with content that is generated to nearly perfectly match the content around it. Similar features have existed in tools like Gimp for a couple years, so the idea is not new, however this is its first encounter with a mainstream product. Along similar lines are two other new features, including automatic lens correction and puppet warp. The lens correction feature can analyze a photo for various types of distortion (such as pincushion or barrel), and correct lines that should be strait. The puppet warp feature is pretty intriguing, as it allows you to mark parts of your photograph, such as a flower, and bend, tilt, or move just that part without affecting the rest. I believe this feature works hand-in-hand with the content-aware fill to keep your picture looking pristine.

Another feature of Photoshop is its Merge to HDR feature. This is probably one of my most used tools in CS3. It has been improved in CS5 to support single-image HDR via RAW (or other high-bit-depth files such as TIFF), better ghost removal, and an improved tone mapping tool.

Another benefit of CS5 is that it has begun incorporating GPU shaders to accelerate a lot of the common operations, greatly improving the performance of the application.