Adult Black Belts go back and focus on the intricacies of the forms and basic material, but also begin a more personalized training. For instance, everyone does a little tai chi, a little more breaking, a little bit of sword and bo staff, a little bit of judo. Just to sort of see what it is about and understand it's basics. But then anyone can choose to "specialize" in any of these and really focus on getting good in the area they like best. As someone else mentioned, we also do a more free-for-all sparring at Black Belt which includes take-downs, pressure points, joint locks, etc (instead of just tournament rules). We have a two hour class on Fridays just for Black Belts (which is most everyone's favorite class of the week).
Pooms on the other hand continue only to focus on basic curriculum only. All kids of any age who test for Black Belt have to have all the color belt curriculum memorized and good, but most of them tend to slowly lose it after testing. So we continue to focus on it, keeping it in their heads and helping them improve. A lot of them also do a lot of tournament sparring, and most of our pooms also make up our demo team, so they may do some new exciting breaks and they also enjoy doing a lot of falling/rolling stuff (running and jumping over something and rolling out). They also enjoy getting really good at flying side kicks!! But our focus really for them is continual improvement on their basics, and working to really keep it all in their heads.
By the way, we do have a couple pooms that are 13 or 14 and they are starting to be included in more of the adult stuff. So while they don't get their Dan until 15, they do get to be included in more adult training when they are ready.