As far as Adobe products go (their professional line anyway) Premiere Pro would be a better choice than After Effects (AE). After Effects is, as alidan suggested, a post tool. Personally, I would not try to edit with AE. I have both and use Premiere Pro for editing and AE for effects.
Premiere Pro CC 2014 supported graphics cards list You will need to scroll down the page to see the supported AMD cards for GPU acceleration. Premiere Pro CC 2014 is available through a subscription only so you can't buy it outright like you can Vegas.
There should be many editing programs that support OpenCL. The following is from a
tech support page for CyberLink PowerDirector:
"Note: Accelerated video encoding on AMD graphics cards requires the user to install the AMD Media Codec Package, also known as the Avivo™ Package. This package is available as an optional download when obtaining an AMD Catalyst™ Display Driver for AMD desktop graphics and notebook graphics products, available at www.amd.com."