I'm more of an old school gamer (although I do play lots of new games), so I prefer expansions. But I think it may depend on the genre. As mentioned in the underrated games thread, there was an expansion for Neverwinter Nights 2 called Mask of the Betrayer which was damn good. You most likely will never see something that long and in depth as dlc. It seems to me dlc is marketed towards the short attention span people. Mask of the Betrayer is a good story that you just wouldn't have time to tell with just dlc.
Now onto a DLC example. My favorite game is Fallout: New Vegas. They released quite a bit of dlc for this game. Because it is my favorite game, I bought nearly all of the DLC (except the courier's stash which are just items you can find I think). That said, none of the DLC for Fallout: New Vegas is as good as Mask of the Betrayer expansion. They are too short. My favorite of the bunch is Honest Hearts (which most fans think is the worst coincidentally), because I find Joshua Graham the most fascinating character of the DLC. Despite that, the dlc is too short to have in depth quests, and not enough dialogue with Graham (and the missionary guy too). I would have preferred a little bit bigger map too.
I also bought dlc for Dragon Age: Origins. I originally held off because the price seemed too high. But last year I was in a DA:O mood again, and wanted something new (something that wasn't crappy like DA2), so I downloaded it. But there isn't enough value for my money. It seems to be less than 1 hour per $1. I know that's kind of an arbitrary number. For most things $1 an hour of entertainment would be damn good, but for computer games I expect at least $1 an hour of entertainment. So if I get 50 hours of entertainment out of a game, I consider it a good thing. Lelianna's song was probably the best dlc, but the drawback of that one is it reuses maps from the original game. Although I liked Return to Ostragar as well. Warden's Keep was alright too. The dlc was good, but a little pricey for me. I only bought about half the DLC available for this game. But I do love Dragon Age: Origins a lot, and part of me wants to rewards companies that make games I like, and punish them for games I don't like. I never bought Dragon Age 2 for example (I played my brother's copy). So I may buy X-com dlc if I'm still playing in a month to reward a company putting out this type of game. Because I want more games like this in the future.
So in summary, for RPG's especially I prefer expansions over dlc. You just can't tell a complete story with just dlc in my opinion. If it's something like weapons only, then I can see. But I generally don't buy that stuff. I only bought the Arsenal's dlc for Fallout: New Vegas because there were achievements associated with it (and they were kind of fun achievements too), and I can sometimes be a completionist with regards to achievements.
For things like MMO's, I never buy vanity stuff (I'm not sure that counts as dlc, however), or stuff to make me stronger. But I've only really played 2 MMO's anyways.
For games like Civ, I still prefer expansions as well. Only because there can be major gameplay improvements with an expansion you generally won't see with dlc. The obvious example is Civ5. I didn't buy any of the civilization 5 dlc. They just don't add enough to the game for me. To me, the heart of a civ game is it's gameplay, not the name and graphics of a civilization. But the Gods and Kings expansion I did buy, because I felt there was some value for my money. And I did get some value out of it (although I think I'm done with Civ5 for good now- it runs too slow on my computer, and it's just inferior to Civ4 in too many ways). Religion was a pretty good addition to the game.
Now onto X-com. I've only been playing 2 days, and haven't finished the campaign. Currently I'm pretty addicted, but will that last? Even the original X-com I didn't play that much. Once you've beaten the game, you've seen almost everything. Although like Civ games, the gameplay is the main draw. The original I'd play every couple months or something iirc. The new X-com has a few problems (they seemed to put so much emphasis on graphics, it seems like they had to make the maps small to reduce processing power I suspect), but I enjoy it. If I'm still into the game like I am now, there's a good chance I'll get the dlc. Although if the DLC is just a couple new weapons, probably not. But if it is more missions and maps, then there's a good chance I will.