With inexpensive and fewer devices and equipment, so take it with a grain of salt. Not trying to open a can of worms, but, I personally, find that different DACs, whether or not if it's the chip itself or units they go in, tend to sound a specific way, and I can only use terms I can come up with mixed with "audiophile terms" to describe them.
AKM = well-rounded, can be overly smooth in parts of the midrange, almost like there's variable peaks and dips, and while being generally weightier sounding, it can go either way when it wants to, kind of airy, bassier, very dynamic in volume, imaging and staging, literally can go almost entirely mono-sounding, to huge and 3D in different tracks, track sections or sources, captures individual instrument tone very well almost to the point of being cheesy or wonky; instrument solos really bring that out.
ESS = harsher high frequencies, almost like the vocalists in tracks with a lot of commotion are piercing my ears (AKMs do this too but it's a different kind of harsh), more detailed or revealing of very delicate sounds, lesser bass, thinner-sounding, more metallic and gritty, can be more pacey, more percussive texture from not being as smooth as AKM, consistent imaging and staging whether narrow or big, vocals have more emotion, upfront, and feel more immersive or "exciting". Overall, I tend to enjoy ESS Sabre more upon first impression, because there's something more exciting and different about how it makes tracks sound.
AKM tends to sound its best with good direct source material, while ESS tends to be highly enjoyable in multiple sources; AKM can too but is picky. Then there's the variable where some units can sound like they want to be like the other, but not quite, there's still that sense of having their typical sound but with each chip and unit having their own overall sound but stick to the general premise of their brand signature. For instance, the ES100 is dryer and harsher than the HUD100 but still have a general similarity to their signature. AKMs to me sound more refined almost too much at times without lacking too much bass even when bright, and there's a variability with enjoyment, but they tend to not be so immersive or emotionally impressive as ESS Sabre chips, at least in terms of vocals, especially upon first impression, but non-vocal instruments are a different story. Keep in mind, all are very inexpensive devices, especially my headphones, so my judgement may not be justified, and it's not like I've had everything to test out because of budget.