The Long and Short of It: Detailed Writing vs. Concise Writing

I've started thinking about this since reading Ashwin's story, Mandelbrot's Limit. I really liked it and thought it was better than either of the two stories I'd written at that time, but Ash thinks they're about even. I had first begun cutting down the length of my work after reading a friend's flash fiction and taking a short story class, but now I'm starting to edge back the other way.

All things being equal—Your story is solid either way, it's descriptive, the imagery is vivid, et cetera—if you have the choice of including every detail that occurs to you or paring it down to just the necessities, which would you choose? If you go back and forth, which is your preferred mode? Do you find one easier than the other, or value one aesthetically above the other?