I've always taken a hard stance that Minecraft isn't even worth considering when comparing it to DF, but I had never really given the game a fair shot and couldn't say for sure until very recently. Bought the game, downloaded it, and now I'm having a lot of fun with it. After a long streak of Minecrafting (Community Pack mods and Hard difficulty to better emulate DF!) I've come back to DF only to discover that the way I play the game is now completely different. Before I had been a very conservative DF player... I would always dig into a mountain and shield my dwarves from the outside world, but now I feel much more encouraged to build elaborate megaprojects and big towers outside. So what if a dwarf dies in the process? I've died plenty in MC hard mode at night, especially to ogres, and lost much, much more and recovered... so losing a single dwarf isn't really all that bad by comparison. My ideas on fortress design have also changed by a factor of ten, and now I'm building them more like citadels than the Kaladim-esque mountain caves that I had been building before. After playing Minecraft, I also feel an increased desire to go colonize the cavern layers...
TL;DR by playing a game which is often seen as DF's friendly rival, I have come to understand and enjoy DF a lot more. The way I play the game has been totally revolutionized, and I'm finally learning that losing really can be fun
It has also given me a lot of new ideas to put to use in DF.
How has Minecraft changed the way you look at/ play DF?