If your kids like musicals, stage shows or watch a lot of the Disney Channel, do not miss DHS. I remember being in awe of all of the backstage secrets that we learned in this park when I was a kid... it definitely stirs up the imagination!
Like PP said, you can see and finish more of DHS in half a day than you can with Epcot. The World Showcase walk can take a long time to browse and experience, and many families I know don't make it all the way around, even in a single day. If you're fine with that, then it could be good to expose the kids to other cultures around the world, and then of course, there are neat fast rides like Test Track and a big attraction like Soarin' in Future World. It's A LOT more walking though, and Fast passes for these rides tend to be unavailable after 1pm.
There are tons of characters right when you enter DHS and at the blue Mickey hat, so you can get autographs from some of the more rare characters. At Epcot, there are the classic Disney characters near Innoventions on the right (not the Mouse Gear store side), and the other characters can found in special photo areas in their respective countries (e.g., Snow White in Germany, etc.).
DHS also has two very cool Disney stunt shows: Indiana Jones Stunt Spectacular (2000 seat stadium) paying homage to famous scenes in Indy movies, and the Lights, Stunts, Action Motor Show (4000 seat stadium) with modified race cars doing incredible ballet-like choreography and spectacular stunts. If you have a son, or a husband, who is into action movies, those would be the shows to see.
If you'll be there at DHS in the evening, be sure not to miss the Fantasmic! (the theatre is located to the left of the Beauty and the Beast musical stage). It's a compilation of a bunch of Disney movies, all wrapped up in the theme of Mickey's imagination triumphing over the evil villains in Disney films. There's a cute Princess portion in the middle of the show, and a special Disney surprise involving a Steamboat at the end!
