*** PHOTOSHOP ***
How Photoshop Pro also allows Photoshop Elements working with image planes, including adjustment layers, and layer masks. It also has 'content aware' tools for repair and to move objects from one place to another in the image. It also seems to have most of the same filter effects as the Pro version. For those who shoot in raw format, it will be interesting, that Adobe Camera Raw is included in the element version. Even features like the 'VerflĂĽssigen' tool are included.
*** *** PREMIERE
The Elements version of Premiere has some sophisticated tools for exposure and color correction (bass / lights adjustment, three-way color correction etc.), some surprisingly powerful tools for audio adaptation (Hall, High / Low Pass Filter, Noise Reduction, compressor etc. ), different effects for superimposing an object in front of a different background (Chroma Key, Luma Key, Garbage Matte, Difference Matte, etc.), the ability to put together time-lapse video from still images, and even effects for motion tracking, text or graphics of movement an object follow permit within a scene. There is also a long list of other effects that I'll rather not use, such as transitions in form of a umblätternden page or various other kitschy things that are often used in amateur wedding video.
*** PERFORMANCE / RELIABILITY ***
Both Photoshop Elements and Premiere Elements to run smoothly on my laptop (Intel Core i7, 8GB RAM, Windows 8). Premiere is certainly was the PC more beanspruchende of the two applications, but problem-free playback of high-quality video even possible in real time, as I worked on Full HD footage (1080p). When I used adjustments and effects in a video clip, they were all rendered very quickly.
All in all I think that the element versions have an extremely good value for money when you consider how much they offer. The best way to get an opinion to offer themselves, is to download the fully functional 30-day trial versions of Adobe to try the two programs themselves.
*** UPDATE FROM 12.21.2013 ***
As some customers ask for 64-bit version had: you need a 64-bit version of Windows, the 64-bit versions of Photoshop Elements and Premiere Elements to install. Otherwise, the slower 32-bit version is installed. To find out if you have the 32- or the 64-bit version of Windows, click simultaneously on the 'Windows' key and the 'Pause' button.