I recently "discovered" Charles-Valentin Alkan, whom I thought had pieces that would rival even Franz Liszt in difficulty. I've heard all twelve, and to this day, my mouth is still agape.

Now is this post about Liszt, Alkan, or your mouth being agape ?
If the latter, make sure to close it eventually, for fear that it might stay like that.
If you have a fascination about extremely difficult pieces, look at Amedee Mereaux's etudes, or more recently, Sorabji's Transcendental Etudes and Opus Clavicembalisticum, or Finissy's English Country Tunes.

For what it's worth, my opinion is that the Alkan op. 39 set is harder than the Transcendentals (at least in the version usually played). The earlier 1837 version of the Transcendentals is probably on a similar level to the Alkan op. 39; some etudes are significantly harder than in the revised Liszt version (good luck to anyone trying to get the opening of 1837's no. 8 to make sense on a modern piano), though some aren't all that much more difficult. Despite all my enthusiasm for obscure music, I can't find much of interest in the Mereaux etudes.

I was actually referring to Liszt's Trancendental Etudes. And yes, my mouth is no longer agape.

Also in the opinion of Hans von Bulow, who lists them for study after the Liszt Transcendentals, et al.

I'm sure you look better for it.

Now which point are you raising about the Liszt etudes ? That they're harder than Alkan op.39, or vice versa ?

I'm saying that I thought Alkan's opus 39 no 10 was harder, until I heard the Transcendental Etudes of Franz Liszt.

Just for a bit of fun, I'll compare the two sets in difficulty one by one (disclaimer: this is personal opinion and whilst I have looked at over half of them in some detail, it is a long time since I have done serious practice on them - and some of the serious practice didn't work out very well, haha).

no 1: Alkan harder - the Liszt is quite straightforward.
no 2: Liszt harder - this is one of the more accessible Alkan etudes and the Liszt is full of difficulties.
no 3: Alkan harder.
no 4: Both difficult and I wouldn't want to offer an opinion.
no 5: Liszt is clearly harder.
no 6: Both are not that difficult but I'd say the Alkan is trickier - I had some troubles with the double notes.
no 7: The finale of the Alkan Symphonie is imo the hardest piece I have ever tried to play, so Alkan harder here.
no 8: The Alkan is harder, by dint of physical effort required if nothing else. Unless you're going to try to play the Liszt like Berman or Villa.
no 9: Pass. I don't feel able to comment.
no 10: Alkan harder, though I think it's not quite as hard as its reputation.
no 11: Alkan significantly harder - the Liszt is comparatively accessible and in this case the Alkan looks reasonable on paper, but a few hours looking at it and you will change your mind.
no 12: They are both extremely difficult but in very different ways. No comment.

Anyway that's just my opinion for what it's worth

Here is how Hans von Bülow saw it in May 1868, writing from Munich (from his Preface to his selection of 50 studies from J.B. Cramer):
...
V. Chopin: Op. 10 and 25, with which may be associated the study of the single Preludes (of a special mechanical tendency) from his Op. 28.
VI. Liszt: Six etudes after Paganini; three concert-Etudes; twelve grand etudes "d'execution transcendante."
VII. a. Rubinstein: Selected Etudes and preludes.
b. V.C. Alkan: Selections from his twelve grand etudes; for the most part more difficult than any of the aforementioned.