Like the first volume, it's a pulp Victorian team-up adventure. It's exciting, horrifying and fun. It's particularly full of H.G. Wells, being a retelling of The War of the Worlds with the Invisible Man selling out mankind and a significant plot role for Dr Moreau.
To me, though, it feels much more Moore-ish than last time. Volume One was a romp. It ended with our anti-heroes all still alive and ready for their next adventure. This, on the other hand, kills two of them, has a third quit out of disgust and disbands the League. It's only technically a happy ending. (The Martians die and Earth is saved.) More specifically, Moore's use of Hyde is closer to the kind of storytelling I'd previously been missing. The Murray-Quatermain relationship is also explicit and uncomfortable, albeit also warm and involving the book's two nicest heroes.
It's not tightly plotted, although that's not really a problem. Issue 1 is mostly set on Mars with people who don't matter and will never be seen again. They're only here because it's a Victorian literature mega-crossover, so presumably Moore either felt obliged to include John Carter and Gullivar Jones or else just couldn't resist. Later, once we've reached the proper story (i.e. Martian invasion), there's lots of epic war machine stuff and not actually that much for our anti-heroes to do. Griffin's choices are shocking, but his presence doesn't really change the invasion's progress much. Murray and Quatermain disappear down a plot cul-de-sac and could have been replaced by carrier pigeons. Nemo and Hyde watch things go from bad to worse.
That said, though, that's only true if you judge on Wells's original (and boring) story framework of "aliens are invading, aliens are invading, nothing else". (It would have been more shocking for its original readers at the height of the British Empire, admittedly.) The characters' interactions are where Moore's real story is. They bring it alive. Griffin is vile. Murray's tough, abrasive exterior opens up to reveal issues and fetishes. Campion Bond, of all people, might be the most horrifying character. "If the rest become a problem, we'll probably euthanise them."
The story's real fulcrum, though, is Hyde. He's compelling, clever and capable of a sort of tenderness, but he can and will switch to being every kind of evil monster.
There's black comedy, e.g. Moreau's grotesque creations. (Look out for Peter Rabbit being eaten by foxes.) See also the laugh-out-loud bonus pages at the end. "Catch Moby Dick. Return to port at square 6 and see a doctor."
I didn't even bother reading The New Traveller's Almanac, though. I flipped through. Volume One's bonus text feature had at least been a story, but this is a tourist's guide. This is probably bad of me and I've been told that there's important stuff in here, e.g. the exploits of the pre-1890s Leagues and lots of worldbuilding for later volumes, e.g. the Burning World, Janni Nemo and Orlando. I'm sure that's true. If I'd read this, I'd have learned stuff. I managed okay when those things appeared later, though.
Overall, I greatly prefer this book to Wells's original War of the Worlds... but, frankly, I'd rate The Twin Dilemma over that novel. Moore's also found an intelligent spin on Wells's logical but anticlimactic ending. Personally, I see this book as the second half of the first and most newbie-friendly League storyline. Volumes 1-2 combined are comparable in scale with Watchmen or V for Vendetta... although, frankly, those are better. There, anything might happen and you're afraid for everyone. This is more of a famous face adventure romp. (It's also possible that O'Neill's deliberately crude style creates some distance, energetic and vivid though it is. You could hardly accuse him of trying to be Gibbons or Lloyd.)
I'm still a fan of the whole thing, though, including that Martian chapter I called redundant. Its Sorns look cool. This initial incarnation also has by far my favourite League cast, although I'm also a cheerleader for the Nemo Trilogy's anti-heroes. Next: the Black Dossier.