Digital offers several advantages to the photographers while working.
1) The ability to see the image right away. This is my favorite reason for using digital capture. It gives me a level of comfort because I can see if my lighting, expression, exposure, etc. are correct right away rather than wait to see the film back from the lab in a few days.
2) The ability to change the ISO ( or the equivalent of film speed) on the fly. This allows the photographer to go in and out of a myriad of lighting situations without having to suddenly change film to match the light levels from place to place at a wedding.
3) A virtually unlimited number of photographs can be captured at an event. This can be the boon and the bane of the photographers’ existence, though, because if you shoot them, you've got to edit them. But it frees the photographer from thinking “I can only shoot 10, 12 or whatever number of rolls of film at this event in order to keep it within budget.”
4) The ability to make black and white and sepia toned photographs from the digital capture. When one shoots digitally (unless they are capturied in a black and white only mode on the Fuji S2) every photograph can become a black and white and/or sepia image. Parents may want an image in color, the couple may want to have it in black and white.
5) Digital workflow. Many photographers now offer what is often called a magazine style (or flush mounted) album. Images shot on film would have to be scanned in order to produce this type of album. While it is totally doable, it adds time and another step in the process. Digital capture elimnates the scanning and often the time spent dust spotting the scan made from negatives. (Though I know of a very talented photographer -- George Weir, who is a WEDDING PHOTOJOURNALIST ASSOCIATION member -- who prefers film and has his images scanned to disk to allow him to still post images online and then create images for his lab. He has created a digital workflow without using digital capture and is very pleased with the results).
6) Freedom to experiment. This is a corollary to reason one. I will often shoot images that I would not even try with film because I know I will be able to erase it if it doesn’t work and modify it because I’ll be seeing the results immediately.
I was on a foreign trip last year and stuck in the bus on a rainy day. I literally pointed the camera out the window and just made some exposures just for the fun of it. And it was fun! Some of those images were totally unexpected and I would not have “wasted” film on it. But because I had the immediate feedback I could see what was working, modify it as I shot and make some different images.
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