Here are a few breakdowns on the new quests:
There are three quests that allow for zero flexibility in building:
Paladin: great reward, good deck, fun deck, but there's only one way to use this quest. Play all of the reborns and add mech deathrattles. There are really no other versions out there. And since they rarely re-use keywords, we might not get other reborns in the future to make the options more interesting.
Warlock: this deck was already built the moment the quest was printed. Plot twist is the only way. Unlike Paladin, though, this one doesn't really work. Also unlike Paladin, however, there is room for future development.
Druid: quest Druid is strong and may be fun, but there is no room for variety. Every quest Druid game plays out the same way. Leave mana for 4 turns, start playing the same bunch of choose ones. Even with more choose one options in the future, this deck is more or less set in stone. There's no way to aggro it, since you have to float mana early.
The other decks work/don't work to varying degree, but they all allow some flexibility in style. You can aim for aggro, midrange, or control with most of them. Priest can only be control, but there are various approaches. Shaman is the ultimate example of flexibility. There are 1,000 battlecry minions in the game, so you have nearly infinitely many combos to play around with.
There are 4 quests that can regularly, easily be completed very early in the game: Shaman, Druid, Paladin, and Rogue. Warrior can sometimes be completed early. Warlock, Hunter, Mage, and Priest all necessarily take a while.
There are 3 quests that are in meta decks - Shaman, Paladin, and Druid.
Shaman in the only quest that is flexible, easy to complete, and good. Some of the other quests check of 2 of the 3 boxes.
What quests have the most potential in future expansions?
Shaman will always be good.
Warlock needs more plot twist synergies.
Hunter has an amazing collection of cards right now and still can't get the quest to work. It's probably not ever happening.
Rogue can complete easily with quality cards, but the reward is weird. The immunity doesn't matter much for aggro, and the damage is too low for control. Rogue would need more weapon synergy cards for this to work.
Mage has tons of cheap spells already. Maybe the reward just isn't worth it.
Warrior...who knows? It's a fine reward, but there aren't ways to build weapon centered Warrior decks right now. It's not fast enough for aggro, and for control, you'd rather have Dr Boom's hero power.
Paladin will probably be exactly as good as it is right now unless they add some variety in reborn minions.
Priest has plenty of potential to improve. Any control support will help this quest.
Druid will probably be exactly as good as it is right now unless they add something ridiculous in the choose one options.