If I was planning on using B2...

...and I wasn't using the Auran Empire, can anyone offer a reason why AX1 would be better, other than throwing some money in the direction of the fine folks of Autarch?

AX1 offers domain and settlement details for Turos Tem. It has trade modifiers for it and the nearby regions, in case your players want to do more than delve and murderhobo.

AX1 has an Extravagant Imperial Banquet table.

AX1 has a plot and reason for monsters to be there other than ‘they live here’, which I don’t remember B2 having.

I suspect that AX1 has a better dungeon than B2 does on a geographical level. (E.g. in terms of faction interactions, secret paths, etc.).I don't have any nostalgia regarding the latter, though. If you do, you might feel differently. The surrounding hexcrawl area has more detail in AX1 than it does in B2. AX1 also has a decent number of eerie or uncanny elements underlying its relatively mundane exterior. Which is nice if you are in to that sort of thing. (I am.)

Given the basic structure of ACKS, I don't know if there is anything extraordinarily novel about AX1. (The obvious contrast is something like Deep Carbon Observatory, which is tremendously novel and often bizarre.) If you have been running games for a while and/or you have an okay imagination, you could probably hack B2 or another starter dungeon and make it be as comprehensive and compelling as AX1 is. But it stands as a thorough encapsulation of how to do low-level dungeon crawls in an ACKS-appropriate way.

It offers way more material. Not only is it longer, AX1 doesn't include a bunch of repeated material from the rulebook, which B2 does. AX1 has a more substantial wilderness area. AX1 provides more gameable NPC material. AX1 provides a far more coherent explanation for the dungeon and its denizens. AX1 has better, clearer maps. There are a bunch of other small things, but suffice it to say AX1 clearly seems to have been designed to address many of the problems, both large and small, with B2.