Aside from being in HD, Tales of Graces F has gameplay tweaks and an epilogue entitled Genealogy of the Future to play through. The first video covers those additions by showing new costumes and accelerate mode. Skip to 1:20 mark to see Asbel, charged up in accelerate mode, wail on an enemy with his newfound power.
This video covers the story. It reviews some of the events in Tales of Graces so viewer beware there may be some spoilers.