I currently own a EMM Labs CDSD/DAC6 combo and a Esoteric X-03-SE.
EMM has a more pronounced and stronger bass. It is good, tight, musical (vs. bloated and single note sounding).
EMM is a very high resolving system but at the same time is capable of a very smooth sound while still being resolving.
Overall, I find the balance of these two systems is more alike than different. I think the EMM Labs that I have over the Esoteric that I have is slightly better in my system.
The Esoteric has better build quality.
The Esoteric will hold its value better.
It should be noted that my Esoteric is a player not a transport/DAC combo, while the EMM labs is the separates combo. I think a better comparison between the two would be the EMM Labs separates stuff (newest) vs. the Esoteric X-01-LTD.
Additionally, it should be noted that with the EMM Labs stuff I own, I would re-clock at the DAC. I have never tried re-clocking the Esoteric via the EMM labs to see if there was/is any impact.
The sound stages for both are excellent, focus, depth, height and width.
In the end, the perfect set-up in my mind may actually be the Esoteric transport (best transport mechanism available in my mind) mated to the EMM Labs DAC. Also, unless you plan to use the EMM Labs as your preamp, I would recommend considering the DAC 6e SE version (which should save you a couple of thousand) over the DCC2 SE.