35 mm or digital camera

I was about to hijack littlek's thread with this but stopped myself.

What are the benefits of 35mm as opposed to digital? My father was into photography with the 35mm (developed his own pictures, had all the lenses, filters, etc) He seemed impressed with the features of the digital camera I gave him at christmas.

This is the camera my father and I have.

Just curious, I am starting to get more involved with pictures and would like to know what I am missing.