[ moved to the Premiere Pro forums ]
Premiere Pro (PP) and After Effects (AE) are both able to edit footage, pull chroma keys and apply color correction. PPis a non-linear editor and so is primarily used to assemble clips into a timeline, so it has a lot of editing/transition and layering tools. AE is a post-production tool for creating very complex visual effects and applying compositions onto footage but it doesn't have the same real-time playback as PP.
Speedgrade is a dedicated colorist application - while it can be used to assemble clips into a sequence it doesn't have anything like the features of PP or AE, and it takes a while to learn how to use it. What SG does have is a very powerful color-grading toolset designed for use in a professional workflow.
If you're doing basic grading of clips from a consumer camera or DSLR (setting white balances, etc) then PP and its Three Way Color Corrector is usually more than adequate. If you're working with pro cameras that record in RAW/log format, Speedgrade is the best choice but you would be using it in combination with PP to assemble the final program.
Dave's answer is well said. Here's the short version. If you have to ask the question, then just use Premiere Pro.