Great thread idea!
I think that what everyone else has said so far definitely *adds* to Halloween Horror Nights' appeal, but nobody's really nailed what makes it super special. You can drink during the day at Universal, you can wander around at night during the summer, and there are plenty of times where the park is directed primarily to adults (Mardi Gras, for instance). I think the true thing that really makes Halloween Horror Nights pop is its ability to create a completely unique atmosphere. Yes, that includes drinks, girls, and rowdy adults...but it's also more. You lose the feeling that you're in a theme park aimed at the mass market where everything has to be "safe" and politically correct. That sort of tension and uneasiness, mixed with the logic in the back of your head assuring you that everything really is fine, is the perfect blend of fun and scares. When you mix all the fog, music, roaming actors, and impressive setpieces into a place that you know so well, it really kind of adds to a the nightmarish quality the event is going for. I think that's the real reason we love it so much--because of the thing you can't really pinpoint.
Unfortunately, the atmosphere and nightmare vibe of turning your favorite place into a weird, scary, unknown territory, has really been lost in recent years. Gone are the elaborate scarezones. The Walking Dead has stolen a lot of the event's great creative aspects. Really, the details that most guests don't notice are what add to the overarching whole that everyone loves so much, and with the new corporate mentality a lot of that has been lost. I still have hope that they'll bring it back, but nothing beats the earlier years where Creative just went all out transforming the park. While there are plenty of other haunted attractions around the country, none went through the same transformation as Universal used to for HHN.