I almost always play at night. I do like how everything looks brighter/the colors are more vivid during the day, but I also like the fact that Dusk Balls pretty much always work well when I play at night. I'm not sure what my favorite time of day is; there are pros and cons to each, though night probably wins out, in part because I've just spent the most time exposed to it.
On another note, I used to love the time of day system back in GSC, but it doesn't seem to affect as many things (e.g., as many Pokémon appearances) in the later games, and I find the visual differences less obvious than they were back in gen II when morning/day/night were first introduced. If anything, I get annoyed by things that have to be done at a certain time of day now, as most of my gameplay (for any generation) now happens right before I fall asleep, so I only see morning if I stay up later than I would like to, and I rarely see day.