Count me in as another person who absolutely loves loves loves DW. Why do I love it? For a handful of reasons:
1) In a world of 4X games that are all essentially the same as each other (build up as fast as possible and crush everything in your path), DW breaks the mold by being an unabashedly complex sandbox. I personally love that I can play the game without the goal of conquering the galaxy (I usually play with victory conditions turned off). It gives the whole thing a Europa Universalis in Space feel, which is a good thing if you, like me, are a huge EU fan. The result is more of a role-playing experience (role-playing leader of X alien species) than a "must optimize my play style" experience.
2) On a related note, the level of customization at the game start is amazing. If you want, you can play in a galaxy with lots of pirates, and advanced interstellar empires as a small, new-to-space civilization trying to make it. Or you can start in galaxy teeming with independent colonies, as an advanced technological civilization that hasn't expanded. Or you can... and so on. The options are incredible, if you take the time to tweak your starting situation.
3) The automation is fantastic. Don't want to manage something? Let the AI do it. It adds even more spice to gameplay. Sure, you can control everything, but you can also, say, leave your entire war machine to the computer, focusing on research and ship design. Or you could do it the other way around. Either way, there's added challenge and, I would say, fun in playing a limited role. Hell, you can even design yourself a single uber-ship and fly it around doing solo pirate raids if you want, leaving the rest of your empire to the AI.
4) The economic system is so wonderfully in-depth, principally because it is not nearly as abstracted as in other games, whilst not being something you have to micromanage. I absolutely love that every component you build requires actual specific resources to get built.
As for the game's weaknesses...
1) The graphics may not be anything special, but they don't need to be. As another poster points out, DW in 3D would be a computing nightmare and, I might add, a player's nightmare. Consider Majesty and Majesty 2. The latter is a more polished game in many ways (fewer exploits, more challenging campaign), but being in 3D gives it no advantage over the original Majesty, which was an ugly 2D game that is, nevertheless, extremely functional. Or consider almost any Paradox game. 3D for EU3? No thank you, it would only get in the way. When I consider a DW merged with, say, Sword of the Stars, it just makes my head hurt (since that SotS galaxy map gives me the spins already) and my GPU burn.
2) It is true that the AI is still a work in progress, as well, but that's to be expected in such a complex game with such a small development team behind it. The AI is, despite its imperfections, certainly competent enough to give you a game, especially if you don't purposely try to use its weaknesses against it.
3) As others have pointed out, the UI and research trees have been greatly improved in the expansion. Also, they've fine-tuned automation.
4) My biggest gripe, still, is the ship design screen. It's just too bland and cluttered. There's not really a good way to tell if you're putting too much or too little of a given component in a design, and there's no good way to compare designs while you're in the process of designing (unless there's something I don't know). So I mostly leave design to the AI, except if I need a very specific ship for a specific purpose.
I think, though, that DW is a polarizing game because of how different it is from the accepted mainstream. It is a game that chooses inferior graphics and greater complexity instead of being shiny and streamlined and easy to play. But it doesn't make those choices out of laziness. Rather, it is a "throwback" only in the sense that it looks old; it is instead as if someone retreated 10 years, and then said "what can we do with all of the increased computing resources since 2000 besides making the game look better?" The answer: huge galaxies with thousands and thousands of civilian ships simulating a real galactic economy of 20 space empires, all running in real time, and zoom-able so that the whole thing takes place on a single map.
So yeah, I'm a fan, if only because so few developers choose to make games in the way that the DW team is making DW.