Battles are solved in the round the occur so only cards you already have in your hand and have set aside on your board can be used so you won't see any prolonged stalemates.
I don't think that it was prolonged stalemates that were a problem in Mythtopia; it was the prolonged stalemates that prevented the game from finishing that were the problem!
- The main thing people complain about with A Few Acres of Snow is the so-called "Halifax Hammer" strategy which is supposedly uncounterable. Much has been written on the subject relating to that game, but the problem doesn't exist in Mythtopia or A Handful of Stars because there's a randomised setup (complete with flaky excuse as to why there's a randomised setup).
- The main thing people complain about with Mythtopia is that between evenly-matched players the game could potentially go on forever. There are various house rules that resolve this in better or worse ways, but the problem doesn't exist in A Handful of Stars because it has a strict end-of-game timer.
- The main thing that people complain about so far with A Handful of Stars is that the player races all have silly names; this will almost certainly be fixed in the game that Fantasy Flight release using the same mechanics in a year or two. So long as you like the Twilight Imperium race names or Star Wars, I guess.