I think they have little to do with eachother, the focus of FE seems to be rather different from that of HoMM6.
HoMM6 focus a lot on the single hero, doing... everything, and heavy on the strategic combat, they have tried to give each unit a separate ability that is interesting (don't agree with all of them), but worst part in HoMM is the online "conflux" crap (yea im sorry, but it really is crap). Also the poor AI programming made so the map designers had to artificially inflate the difficulty by increasing AI's ability to produce troops the longer you go into the game.
FE Focus on Strategic Depth, every choice should have meaning, you mess up in the start you can feel it lategame. (depending on the mess up ofcourse).
Right now its still in beta, so the Tactical combat is not too interesting, and missing some stuff overall that gives depth. But still have a very decent city system, a huge research tree, and interesting encounters on the overland map. There is only skirmish maps in the current beta, but the maps are randomly generated to provide lots of fun!. Balance is ofcourse not too highly prioritized yet, so you may encounter something ridiculously easy to beat, or something that seems majorly unfair.
On average, the FE beta is slightly better than HoMM6 if HoMM6 conflux works properly (does at my home... now)
Best part of FE right now is it gets better as they patch it 
Sincerely
~ Kongdej
