Yes, there is a choice. The difference is night a day. Camera equipment, how the pictures are processed and even the knowledge of how to shoot a picture is completely different.
Film photography is now considered a thing of the past, yet some photographers swear by it and only shoot with 35mm film. It can be time consuming, though, as once you take the pictures, you have to wait for proofs to come back from the developer. Even if the photographer has his own darkroom, there will still be a waiting period. Once the final prints are chosen, there is an additional waiting period to get those back as well. If mistakes are made, the photographer might not see them until he gets the proofs back, then, he will have to reshoot those pictures. If additional shots want to be taken, then that adds to the timeframe. Black and white film, though, can be worth the wait, if photographed correctly, it can look like artwork.
Digital photography, on the other hand, is almost instantaneous. The bride, parents or whomever wants to see them, can view them through the lens of the camera immediately. These can even be emailed to a computer, tablet or phone. There is no waiting for proofs to come back, If mistakes are made, they can be corrected right then and there. If the photographer has the capability to print out the prints, delivery can be even quicker than film, within hours or a day versus several days. Some digital photographers choose to use a 3rd party to print the photographs, so it might be additional time, especially if bigger sizes or multiple prints are requested.
Quality can be the same on film and digital. It really is a preference by the bride or family being photographed as to which one they prefer. Most, not all, photographers only shoot digital, so it would be a good question to ask when seeking out a photographer as to which medium they use. Some people still want to have their memories on film, along with the negatives so they can reprint them as needed. Be aware though, as technology progresses, that might be harder to do.
Digital photography, however doesn’t need to be taken to a photo lab or print shop, (unless you want different sized photos). Once the photographer is done with the shoot, he can save or send you the prints via email or on a flash drive. From there, you don’t even need to print any pictures, they can be emailed to family and friends and they can print what they want, or better yet save to their computer and use the pics as wall paper if they wish.
Even though it is a choice, technology is evolving to where film might be thing of the past.