The snowball problem in Conquest isn’t really prevalent in games with skilled players. While things definitely feel snowbally for the first few games, this ends up going away with more experienced play - much like like the “runner is really bad!” (because they aren’t running) problem in Netrunner or the first turn giant shootout problem in Doomtown.
Having played both Conquest and Thrones at a high level, I can say that Thrones seems more snowbally at present, since the cards that actively punish being behind (Marched to the Wall) are stronger than the relatively few cards that help you come back (Wildfire Assault). Most of my Thrones games, even against skilled opponents, are clearly over within two turns or so, with one person so behind on board state that they have no real chance of coming back.
Now, to be fair, I am playing fairly aggro decks - but my experience has been that Thrones snowballs very hard, especially on early military challenges or kills from other sources (Dracarys! for instance). I also have high hopes for the future cardpool - in particular First Snow seems like it will be very helpful here.