My kids are 13 and 9 and we have been cruising Disney since 2007. So they were 9 and 5 on their first cruise. They enjoyed it then, but they LOVE it now. And we do Disney on years we don't cruise. Heck, we do Disney when we do cruise.
They love them both for different reasons. You're right the World has rides, but the cruise has focused entertainment just for them. The kids clubs are the best in the industry. There are planned activities for them to do such as pajama parties with characters, making flubber and a graduation at the end of the cruise that will bring tears to your eyes.
You may come back late one night to find your youngest pooped out on a cot or I came back and found my dd bonding with the girl counselors and painting her nails. Often she would tell me to leave her longer and come back much later. lol
They make crafts that they can take home too.
Now the my dd is a teen, she just can't wait to try out their teen only areas. They even have a teen only spa on the Dream.
The World is great, it's just GREAT in a very different way. I would suggest the 7 day cruise or at least the 5. Anything less and you'll just be getting settled when it's time to get off. I highly suggest going over to the meet & greet threads once you decide on a cruise. Tons of families with kids of similar ages are on there and they can make friends even before you sail. I also suggest doing at least 2 days before or after your cruise to do a few of your fav must do's at the park.
I think thats all of my advice. I gotta go pack, I leave this afternoon for Orlando and our Dream cruise/the World vacation


Hope I helped shed some light on your question.
Karen