Don't they all just use multi bits to reduce noise and increase linearity - solving some delta sigma issues? The implementation may be different but general concept is the same.
Not really no. Linearity groups together all sorts of issues and you can address specific types of nonlinearity such as harmonic distortion (or to go down further, specific types/orders of harmonic distortion but not others) but in doing so suffer tradeoffs in other areas like noise or how certain behaviours become signal correlated.
Pretty much all modern DACs are multibit, there are very few true 1-bit DACs remaining as the challenges associated with it are significant. But even on absolutely identical hardware, just changing how the modulator works in order to prioritise different things will change the behaviour of the DAC. Delta-sigma is a maths-driven process and you really can't tell much about a DAC just by looking at the hardware, or even by static measurements. More dynamic testing or exploration of the theory is required.
dCS, Chord, ESS, AKM, and just about everyone else is doing multibit and are taking different approaches to address the issues they feel are important, but they're not all taking the same approach and they all have different advantages and tradeoffs.
For example dCS seeks to reduce signal-correlated behaviour, potentially at the expense of increasing random noise/error.
ESS seeks to reduce some specific types of signal-correlated behaviour, they've gone to great lengths to eliminate changes in performance vs DC offset for example. But at the expense seemingly of increased higher order harmonics.
Chord aims to prioritise transient reconstruction/timing and they do that very well, but potentially at the expense of higher 2nd order harmonic distortion for example compared to some other designs.
dCS doesn't provide too much info about their underlying processes unfortunately, though Rob luckily goes into significant detail both on head-fi and in talks and interviews. (I will be posting his DAC topology talk on YT soon, it has a lot of content relating to this discussion and the challenges facing certain types of DAC topology).
There is no perfect DAC, and there is no free lunch in terms of how you make one to reduce various issues. You have to make tradeoffs and have to pick the things you feel are important. As a result, different DAC manufacturers have DACs that behave and sound different because they're all doing things very differently even if on the surface the hardware might look similar, but under the hood the maths is incredibly different. Hell just ask people how much of a difference the 'V2' dCS mapper made to their DAC.
I should add that for transparency, I don't own a DAVE, but personally I think Chord is doing a better job than others in many ways, primarily because Rob isn't letting available compute power get in the way of the designs. Other manufacturers are seemingly not as willing to use more powerful (and more expensive) FPGAs and ASICs to allow for higher performance processing. But Chord are. And at the end of the day, whilst you can't have a perfect DAC, more processing power does mean that you can sacrifice less in sound quality or objective results.