I was lead to DF after playing Minecraft for a pretty long while. I picked up Minecraft again after playing DF for a few months now, and I gotta say, I was just a little bored. Minecraft is a great game, and it's a lot of fun if you can keep yourself working toward something... but I really lack for motivation and creativity. When I play, I build little holes-in-the-wall hideouts and end up either right above the adminium level, trying to collect as many diamonds as I can, or throw everything to the wind and just wander around in caverns or outside in search of interesting quirks in the world generation. Those are both very fun, but for me they can wear a little thin after awhile ("How many stacks of diamonds do I REALLY need?," "How many hanging-mountain-cliff things have I seen before?"). I can see how smart, creative players can get almost unlimited fun from the game, but the kind of stuff I want to do with the world ends up being somewhat monotonous or pointless.
Also, after playing DF, Minecraft just doesn't seem to have enough meaningful variables. All that cool stuff you can do with the physics and different blocks, but a lot of the time I felt like those things existed for the sake of themselves alone (how I've heard people describe the whole game, really). Right before I set down MC the first time, I built a pretty big compound with a neat furnace building, house, glass overlook, and a massive storage building, but I got frustrated when I realized that the 10x10x3 room I dug out at the beginning of the game served essentially the same purpose, but without a bunch of walking around. The satisfaction of looking upon your own well-designed creation is sort of lost on me. Roleplaying was fun for awhile, but again, variables... I'm a wanderer or I'm a developer, and I never saw much to do with those that wasn't without some relevant game feature to add the experience (nutrition? value? real or diverse danger elements?).
I don't think the two games are easy to properly compare, but when you get down to the refuse-gravel, you're doing the same sorts of things in both--diggin' down and makin' stuff. They are both really fun, regardless of which I prefer, but DF is just more interesting to me as the sort of player that I am.