The Edge has the same 2.0T that has already been discussed in this thread. The Edge ST has a 2.7TT V6 engine.
I personally dislike the transmissions in the Edge. It is an 8 speed, which uses the same exact ratios as the 6 speed it replaced, but with additional gears added (second and eighth). This causes its progress through the gears to feel awkward (as if the 6F35/6F50 wasn't already awkward enough). The 6F trans that the 8 speed is based off of have been reliable enough, but are plagued with abnormal transmission behavior. In my short time in the vehicle, I feel the addition of the two ratios has only exasperated this issue.