This question and answer have been on my FAQ since I first started my business, back when digital had just overtaken film in terms of popularity for wedding photography, and although it's been revised over the years, it's quite obsolete at this point, since although there are still some niche film shooters, virtually all wedding and portrait photographers shoot digital now, and digital photography is established and mature enough so that most people feel perfectly comfortable with it. But I'm leaving it up just in case anyone might still be curious about this.
The quality of images from professional digital SLR cameras has for quite some time exceeded that of 35mm film, and quite dramatically so in terms of the ability to shoot in low light. In addition, in the hands of an experienced photographer there are numerous other operational advantages provided by digital in the fast-paced and unpredictable environment of photographing weddings, particularly with not having to switch to different types of film when lighting conditions change (as they very often do throughout the course of the wedding day).
Digital also provides for a level of protection for your precious wedding photographs not possible with film. My cameras capture to two memory cards simultaneously, providing an instant backup that drastically reduces the chances of image loss, and digital photography enables me to, within hours of the conclusion of your event, have additional multiple backups (including an off-site cloud backup). All this was simply unfathomable in the film days where only one true original (the negative) existed, with prayers being said by the photographer in hopes that no rolls of film would be destroyed or damaged during chemical processing. Any other copies or prints from film-shot images would be of reduced quality, while there can be an infinite number of backup copies of digital images that are exact duplicates of the original.