Kids and adults are by definition at different stages of life and world experience. Little kids in particular are balls of energy waiting to be released. They have not learned inhibition yet. They want to be loud and to participate Big Time. Adults are generally more laid back and socially restained.
When I do a kids show and ask for a volunteer(s), pretty much every hand in the room goes up and shakes back and forth wildly in the air; there is almost desperation in their little faces - that's how bad they want to participate and be involved. Adults - (with some exceptions) not so much; they generally prefer to kick back and watch.
Then there are the differences in what interests kids versus adults. Look at the differences in the movies, TV shows, books and games that are geared toward and popular with kids, versus those for adults. So, to successfully entertain a group, you need to give them something that they can relate to. It's not so much a question of what trick, as it is how that trick is presented. What will they relate to? That is the key question, be it kids and adults. Take the cups and balls for example. I have used a Harry Potter type script, or sometimes Power Rangers, for kids. The 3 balls are Harry, Hermione and Ron; the cups are their rooms where they hide from Lord Voldemort. I got my wand from my friend Dumbledore last time I was in Diagonalley. The kids magically disguise themselves as pieces of fruit at the end, completely escaping detection. You get the idea. Compare this to say, Ricky Jay's sophisticated version of the cups and balls based on going through a history of the routine. Appealing and fascinating to adults - but would bore kids stiff. Or a card trick done with Pokemon cards will stir kids' interest and enthusiasm, (or for younger ones, alphabet cards), while many things done with "regular" playing cards, other than maybe simple color changes and other quick visuals, will leave them flat, as Antonio pointed out. The same holds true for Professor's Nightmare - for kids, I do it as Trevor Lewis' "Stop, Look and Listen" routine, with heavy involvement and participation on the kids' part, whereas for adults, I use a "hypnosis" theme, which they can relate to, and a kid generally would not.
Whether it's kids or adults, the performer needs to have an understanding of psychology of the (little or big) people for whom he/she is performing and know how to apply that psychology to make it fascinating and entertaining. And as Christopher T observed, even what will work for one particular demographic of adults will not necessarily work for a different one. One size does not fit all!