In general, I prefer Crossword puzzles, mostly because crossword puzzles can go meta and have themes and be puzzles-within-puzzles. And because, if I make a mistake in a crossword puzzle, I can figure it out from surrounding clues, but if I make a Sudoku mistake, I basically have to scrap the puzzle and start over, which seems . . . like bad management, I guess?
Which might explain why I'm fond of BrainFreeze puzzles (and am a huge Laura Taalman fan, in general) -- because she and other mathematicians create funky variations on Sudoku that make me think hard. Like this puzzle by David Nacin I started yesterday. The pink squares have no clues at all, and the white squares have clues between squares iff the sum of adjoining squares is prime. Ouch, brain hurts in a good way.
That all being said, Sudoku is a lot easier to do communally on a chalkboard than a crossword puzzle, because it's so self-contained, so it's more fun to do with other people --- provided you happen to have a chalkboard in your dining room, of course.. I've been getting N-son hooked on the Monday & Tuesday newspaper Sudokus, and having them up on the board makes it easier for us all to work together. I'll suggest hints, or warn him off of errors, or what-have-you. It usually takes him a few days, but it's some good back-and-forth entertainment for us.