HK is significantly worse than Dragonfall in just about every way:
- The writing is worse. Lots of non-interactive text dumps really dragged the game down. There was a lot of writing in Dragonfall, but people didn't just dump their entire life stories on you like in HK. HK also has a lot more LOLzy writing. Take the shadowland board, for example. In Dragonfall it feels like a place where runners would go and trade gossip, but in HK it feels like a stupid reddit sub.
- Encounter design is much worse in HK. HK enounters are mostly a bunch of weaker guys rushing at you (and I've heard Battletech is the same). To increase difficulty they merely upped the number of enemies, and the higher amount of enemies (like in the tower extraction mission) can make the wait between turns painfully slow. In contrast, it felt like effort was made to make many of the Dragonfall fights unique and challenging (at least on the highest difficulty). Blitz's mission has you taking on another team while Blitz is in the matrix trying to juggle between taking on another Decker and trying to turn the turrets on to your side. The cybertroll mission gives you a super-powerful ally, but one who will become an enemy if you don't take out the enemy hacker fast enough. Sometimes you fought a number of weak opponents, but sometimes you also fought fewer strong opponents (the mercenaries, the basilisk). It might be my imagination, but enemies also seemed to use cover a lot more.
- The matrix is worse in HK. Though the first two games had a pretty poorly designed matrix, Dragonfall managed to squeeze something decent out of it, with some interesting puzzles (like the bit puzzles) and encounters (like Blitz's fight with the other decker). The matrix in HK was so bad I stopped hacking and started brute forcing everything (which actually lead to the one decent fight in the base game).
- The non-combat gameplay is worse in HK. In Dragonfall there are parts where you have to use kiosks to do research, you have to explore someone's desk to guess their passcode, where talking your way through people involves choosing the right dialogue options and no just a simple skillcheck, etc. You get a couple of interesting things like this in HK (like searching the phone in the bonus campaign), but they're much fewer.
I could go on - much better C&C in Dragonfall, better use of e-mail (felt like an afterthought in HK), better designed main hub, etc. I think the only thing HK improves upon was that the premise for the missions were more interesting. But that doesn't make much of a difference, since the premise for the missions didn't affect the gameplay. Sabotaging fengshui (for instance) is just wandering around a building and clicking on whatever pops up.
Originally Dragonfall was simply supposed to be a small Berlin module, but then HBS decided to let it be longer because of the disappointment in SRR. Then they released an extended edition based on the positive reception. My guess is that Dragonfall is better because it was built with a small team of talented individuals. Having the uppermanagement directly in charge of HK and adding a bunch of other developers only succeeded in making HK worse. It's telling that the best game coming from HBS - the only truly good game they've made - is the one whose development team was most disconnected from the rest of the company.