I'm a librarian who loves anime, manga, and reading a wide variety of genres.
This first volume is crammed full of stuff – the Abyss, Chains, the coming of age ceremony, the Baskervilles, Pandora. Just a little bit too busy for my tastes. I don't know what I would have thought of it all if I hadn't already seen the anime. I did think there were some nice aspects, though. For example, I liked the whole setup with the Chains, and Oz's friendship with Gil was good (although Oz does occasionally look like a bully).
From what I can recall, the anime and manga seem to be very similar. The anime had some extra padding – I'm pretty sure the part with Oz's time in the Abyss was shorter in the manga.
There are technically several Alice in Wonderland references – Dee and Dum, Alice, B-Rabbit, plus more to come later on – but the connection is so light that I'm not sure why Mochizuki did it in the first place.
(Original review posted on A Library Girl's Familiar Diversions.)