DC removes piss yellow fullscreen filter (BY FAR the best change they made), makes you have to pick up some of the cheater DLC items, integrates* Missing Link into the main plot where it belongs, and the boss fights are marginally improved. The bosses still suck though, except for #4 which was already pretty cool in the original game (hint: bring a laser rifle). In exchange, it removes several patches' worth of bug fixes because the game is basically a port of the WiiU version and not really an enhanced version of original PC game. It also makes the game extremely easy, due to getting so many praxis kits after Missing Link that you can max out everything from that point on. You also have to play on the hardest difficulty--which you should anyway as both the original and DC are sorely lacking in challenge--to get rid of the game-breaking two-cell recharge.
Avoid the DC at all costs imo, the trade off is not at all worth it.
* - "Integrates" used very loosely here. It's not really any different than getting to that part, quitting DXHR and loading up Missing Link and playing through it before returning to the main game. The difference is you get a bunch of extra praxis points at the end in the DC, which as I mentioned above just trivializes an already easy game even further. The DLC still functions the same as before, in that you wake up with no augs and have to get them back and then when you finish it you basically have to respec Jensen before continuing on in Panchaea (with a bunch more points to spend).