In my humble opinion, I think the best part about digital is the quantity! I have the freedom to take hundreds upon hundreds of photos before I need to give any thought to the space on my memory card. This gives me the freedom to try the same image multiple times from different angles. Or trying several different variations on the same pose. That's a big change from when I used to shoot weddings on film and was limited to 36 frames per roll. Of course I would bring a large quantity of film with me to shoot, but I had to always keep in mind how many shots were left on the roll before I needed to change it out. That meant conserving shots during the ceremony so I wouldn't miss anything important (like the Kiss!) because I was putting in a new roll of film. Can it be done successfully? Of course! But is it better not to have to worry about it at all? Obviously!
Here's an example of an image that didn't quite turn out the way I envisioned, but am still grateful I got to try. At this maternity session I told Daddy to kneel and pretend to "catch" the baby. However the family quickly fell into a fit of giggles and we didn't quite get the shot. But since I wasn't worried about having only a limited number of shots, we were able to have a lot of fun during the session and try different things, wether they turned out perfect or not.
I'd love to hear your thoughts on digital vs. film photography in the comments section. :)