What I like:
- Big number GOOD. While I appreciate the elegance of "roll under" systems, I just can't get on board.
- Quick results. If you are using target numbers, they should be known.
- Degrees of success.
- Skills that can be improved.
- Not having to wait for people to do lengthy math calculations at the table.
This can be accomplished with percentile systems, d20s, dice pools that track "successes," "dice ladders," or a small (2dX-3dX) additive dice system. It may sound silly, but I've had smart players who struggle with adding up more than 3 numbers. Exploding dice seem to be an exception to this, but that may be because the minute a die explodes, everyone's paying attention to the results so it doesn't FEEL like the math takes forever.
Personally, I love the swinginess of the d20 or "exploding dice," but I know not everyone does.