Brume Tower is actually full of various gimmicks and things to do. AotA is mostly a straight path to Manus. AotA has better boss design but shit everything else.
I'd go a step further and say Crown of the Iron King pretty much trumps AotA on all fronts.
AotA level design is decidedly below median for Souls games. The Dark Chasm is rushed crap and the Royal Woods are a reskin of Darkroot Garden minus the inter-connectivity that made it interesting to traverse and the moonlit forest motifs that made it puhwetty to look at. The "best" area is the Township, which is a mostly linear romp towards the Dark Chasm, filled with the same "encounters" Dark Souls 1 recycled over and over: clusters of hidden meleed00ds placed to punish players sprinting through the level and (multiple) ranged attackers in awkward spots, like enclosed rooms or while doing tightrope walks.
Brume Tower blows this out of the water. There's a ton of verticality in the level design, plenty of elevators to turn on, hidden alcoves to drop into, walls to destroy with explosives, and all sorts of other cool stuff.
AotA enemy design is rather lacking. The Humanity Phantom is one of the laziest designs in the entire series and everything else is some sort of one-dimensional meleed00d or a Bloathead Sorcereress, which mostly did nothing but spam Dark Orb (it almost never casts Dark Fog). Oh, and there's an invading phantom with a cool, but ineffectual special attack.
Contrast with the inhabitants of Brume Tower. Sure, the Ash Soldiers are rather generic, but the Fume Sorcerers, Iron Warriors, and Possessed Armors are terrifically designed enemies, some of the best in the series. The Barrel Carriers and Crawlers are interesting in the way they play around with environmental fire as well as fire attacks, giving the player a chance for easy chain kills or to do tons of damage to other enemies if they're smart about it. And the way in which everything interacts with the different Ashen Idols is a stupendous way of mixing up enemy encounters and melding the explorative and action elements of the game together; finding more Smelter Wedges allows you to "turn off" enemy buffs, curse zones, regeneration fountains, and Firestorms.
Bosses are really the only area in which AotA can even come close, and I'd still give the edge to Crown of the Old Iron King, even though the entire boss roster of the DkS2 DLC would be more appropriate given that AotA sold for twenty KWAbucks and each DkS2 DLC retailed for ten KWAbucks.
Both Fume Knight and Sir Alonne (along with Burnt Ivory King) do the "player-versus-knight" fight a lot better than Artorias. They both have movesets as deep and comprehensive as Artorias (if not moreso), and are far more fun to fight repeatedly due to the way they're attacks are less predictable; both can branch out their combos in different ways and slightly alter the timings of their attacks, having a variable amount of frames between the startup telegraphing of their attacks and the execution. That's huge in a game that basically reduces to dodge/block->jab, forcing the player to pay attention as opposed to run off of muscle memory. Faster action games like Ninja Gaiden, DMC, Bayonetta, etc. can get away with consistent windup into attack animations because they're blisteringly fast, but a slow-paced series like Souls doesn't have this advantage. "B-Team" (lol @ this pejorative and the people that use it unironically) came up with a really solid solution.
And this is coming from someone who loved Artorias forall the Devil May Cry references he sported (mostly notably Stinger and a "Devil Trigger" complete with the trademark purple aura and a DMC#-style DTE).
Kalameet was fun, but Sinh (in Sunken King) was a
much better dragon fight, probably about as good as Souls games are going to get...they're not built to handle Dragon's Dogma types of shenanigans. Sanctuary Guardian was forgettable, kind of like Blue Smelter (who at least had the sweet windup-to-attack frame variance, even if he was a legit reskin). And Manus was overrated trash, unpopular as that might be to state.
I could probably continue this comparison with things like itemization or visuals, but I don't think it's really necessary at this point. AotA really doesn't compare well.