I really like a stick blender.
We used to use a regular blender that had a food processor attachment too. Anytime we wanted to use the blender we had to search for all the parts and assemble it. Then when we were done we had to disassemble it getting all messy, and all the parts would take up half the dishwasher. We used the food processor attachment quite a lot, but it was very small.
We decided to switch to a bigger more useful dedicated food processor and get a stick blender. We have been so much happier with this arrangement. The food processor parts are all hard to loose and there are fewer of them most of the time (it has extra attachments for various jobs, but you don't use them all at the same time as you do with the blender.)
The stick blender is perfect for making a quick smoothy. There are only two large parts, the motor and the wand, so nothing goes missing. When you are done you can just press a button and let it drop straight into the sink. You can let your DC (no matter how young) put all the ingredients into his own cup, since there aren't any blades in the cup itself. You can make different flavors for everyone without cleaning out the pitcher, since you can use many containers, and not just the one that it came with. If a frozen strawberry gets stuck on the blade, you can just pull the wand out of the cup and clunk it on the side of the cup. You don't have to poke down through a pitcher full of half made smoothy with a long spoon just to get to the blade area.