The simple answer: No there is no such thing as a universal "X is better than Y" in exalted ever.
The more elaborate answer:
Things in Exalted are not easy, because Exalted is not D&D. It is neither WoD, it is Exalted. There are no vulnerabilities shared by all beings of the same splat! Like, no, not all Alchemical Exalted are vulnerable to fire effects, not all DragonBlooded succumb to Poison X and not all Lunars do love their Solar mates (I'm looking at Lilith here...). There simply*is no thing like a Pokémon weakness grid in Exalted.
Atop that, beings in each of the classes scale extremely wide. Let's take undead for an example:
- On the low end, there are Zombies and Hungry Ghosts, that even in bigger groups aren't a real threat to newly exalted Solars - but if you get an army of some thousands, then a circle of Solars might start to sweat.
- On the high end, there are Nephwrack, that have Essence 5, 19 Health Levels and 100 motes. These Undead Prophet-General-Kings can cause serious harm to a circle of 5 seasoned Exalted or even kill them.
You can't put those two into the same box for any other thing than "both are undead". None shares the same weakness with the other even in this box, some don't have charms or something similar, so comparing them beyond general power level is moot.
Now, looking at Fae is somewhat different and more troublesome, because Fae don't just scale in their splat, but also where you are, but for that see below. Also, Fair Folk, Wyld-Mutants and stuff like Hobgoblins are also all handled in the "Wyld" bracket or enemies, so they are highly variable again. Some of these (Hobgoblins) have weaknesses, most don't.
So, there is no universal weakness... at least usually, because there are two exceptions: Artifacts and Places.
There are weapons that all beings of some splat are weak against - however, that is not because of the beings having a specific vulnerability against this weapon type, it they are weak against. It is the weapon artifact, that is specifically made to harm these beings, and these weapons (usually Daiklaives) are pretty unique and rare.
To some degree this also holds true for various places: The Underworld has specific effects on any being in it, but what this is depends on if the target is alive or undead, Malfeas does so for hell origin or not, the Wyld handles Wyld creatures different (empowering them) from anything other (it tries to warp everything else). Even Creation handles beings of Underworld/Malfeas/Wyld origin different (generally weakening them over time) from anything else. Yu-Shan has special rules that are different for Gods and other beings... To sum it up: Almost all places do handle things differently for specific splats, but that doesn't count as a collective weakness.