From what I have read elsewhere, I agree that the Audinst beats in the Aune in various aspects, especially the DAC section. To be fair, the HUD-MX1 does cost a bit more.
But in terms of upgrade path, the Aune comes out on top. It has 2 socketed op-amps versus the 1 socket in the Audinst. It has RCA analog line-in jacks, so you can upgrade the DAC separately. And it has an SPDIF input, while the Audinst as an SPDIF output. So the Audinst can only ever be used with a computer, while the Aune is more versatile. Its power supply can be upgraded, as can the Audinst's. However, the Aune's DIY roots means you'll find sweet mods like the ±10VDC dual regulated power supply. (Takes a bit of work though, unless you buy it pre-modded.)
Objectively, there's probably some owner's bias affecting me. I own an Aune, and have not heard the Audinst. And from all the positive reviews I have read, I can accept that in stock condition, the Audinst HUD-MX1 sounds superior to the Aune.
PS Thanks bearmann. It's a picture of Shanoa from the Castlevania: Order of Ecclesia game. I used to have an actual Dhalsim yoga flame as my avatar, but for some reason it got removed.