We just got our digital camera and haven't taken it to Disney yet, but we have used it for a few other things already.
The digital has a bunch of advantages over the 35mm.
1. Its small enough to carry in my pocket. Our 35mm is big and bulky and really a pain to carry around your neck for any period of time. It also came with a nice case that loops through my belt and holds the camera, batteries and memory cards.
2. The 256MB memory card I bought holds 260 high resolution photos, more than enough for virtually anywhere I'm likely to go. Consider that is equivalent to almost 11 rolls of 24-exposure film. So not only is the camera easier to carry, I don't have to carry a bunch of film too.
3. I can delete photos that don't come out well immediately and save space for the good ones. I only need to print good photos so no money is wasted printing pics that aren't good.
4. I can go to many stores and print my photos by popping the memory card into the kiosk and following a simple process. I've already printed photos at my local Target for $.27/print. That is as cheap (or cheaper) than processing 35mm film and, as noted, I only print the photos that I want rather than having to pay for and print every picture I took, good or bad. If I'm on vacation and fill up the memory card, I can find a store, print out the photos and/or burn them to a CD and clear the memory card to shoot more.
So what's the downside? I have noticed that red-eye is a significant problem. That never occurs with my 35mm because the flash is not near the lens. On the other hand, it only took me about 10 minutes to edit out the red-eye on a batch of about 50 photos I took last week so it is a bit annoying but not enough reason to switch back to film.
The only time I would probably choose the 35mm is if I was going to be taking action shots - sports, dance, etc. There is a momentary shutter lag on the digital that doesn't exist on the film camera.