cracks my fingers
We see in War of the Ancients how fel hunters’ draining ability works precisely. They don’t simply consume mana, but magic as a whole.
Malfurion cried out as he felt it begin to drain him of his power. It mattered not whether a spellcaster was a sorcerer, wizard, or druid, the magic that they used quickly became a part of them. By draining it out of its victims, the felbeast also devoured their life force. Given time to finish its unholy meal, the felbeast would leave only a dried husk.
When you use a type of magic - any magic - enough, it intertwines with your very life essence and draining one drains the other. We also see in War of the Ancients that a felbeast makes an attempt to rush Tyrande and her priestesses (though it gets intercepted and killed by Dath’Remar) with its tentacles out so they at least tried to consume the Light, and Tyrande & Co. seem convinced that yeah they actually could, thanks Dath’Remar for saving them.
When the felhunter has devoured enough magic, they multiply. One felhunter can quickly become an epidemic if it’s not stopped in time.
Malfurion screamed as the vampiric suckers literally tore the magic from his body much as the teeth would soon tear his flesh. To any spellcaster, felbeasts were an especially insidious foe, for they hunted those with the gift for magic and drank from them until nothing but husks remained. Worse, given enough energy to devour, the demonic hounds could multiply themselves several times over, creating an epidemic of evil.
We also see in the same novel that they can devour Fel from Demon Hunters (and therefore warlocks?) but the realisation of what energy the felhunter was dealing with made it fearful and try to pull its tentacles back with panic – but Illidan wouldn’t allow him. He forced the felhunter to stay on while he began to devour the felhunter instead. Uno reverse card.
The motif of magic use saturating your life essence repeats in Rise of the Lich King where Jaina states that Kirin Tor had for years theorised this same concept applying to Necromancers where immersing yourself with necrotic energies slowly turned you undead overtime, and eventually you’d reach a point where the necrotic energies were the only thing holding your body together. At the moment of your death, those eneriges are released, and the necromancer decomposes years in a matter of seconds.
This theory is confirmed to be correct when Arthas killed Kel’Thuzad and his cultists the first time. So it’s confirmed to apply to at least Arcane magic, Life magic, Death magic, and Fel magic. 4/6 of the roster, so we can assume Light and Void as well - though strictly speaking, that’s conjecture until otherwise stated. Though granted, the Paladin ritual does make the Paladin literally One with the Light so 
And finally in The Last Guardian we see that felhunters aren’t inherently immune to magic – their ability to devour magic is an active ability they must channel, performed through their tentacles. Khadgar blew the side of one right open with an arcane blast when its attention was turned elsewhere. What we do see is that their skulls are actually immune to magic as spells ricochet off of them. It’s when the felhunter’s attention is on you that they start consuming magic with the tentacles, but their low profile and their prominent skull makes it difficult to fight one facing you head on with magic.
The one instance where we see a felhunter objectively fail to devour magic is against druidism. And by that I mean when the druid (or shaman) simply asks nature to do things. There’s no magic involved in asking the nature to do things to you as a solid favour, as the felhunter quickly finds out. It’s just trying to eat wind.