Film vs. Video

During the first century of photography and moviemaking, everything was shot on film – a celluloid material whose light-sensitive surface could record lasting images. Film was good because it was the only option. And during that first century, it did a fantastic job of recording those masterpieces that we love and treasure, like Gone With the Wind, Citizen Kane, and The Godfather.

However, as technology advances, digital filmmaking gains dominance and poses a threat to the film hegemony. The Oscar-winner Social Network (2010), for instance, was shot on the Red One, a video camera.

Why Shoot Film

Film is still preferred by most filmmakers because this is the tradition and the technology they understand. Other two big advantages of using film are (1) depth of- ield and (2) broad exposure latitude.

Depth of Field

When shooting 35mm film, shallower depth of filed is a given. This means that creating areas in the frame that are soft focus or blurry is easier, and filmmakers love this to direct the audience's attention.

Exposure Latitude

Wikipedia defines exposure latitude as "the extent to which a light-sensitive material can be overexposed or underexposed and still achieve an acceptable result."
Basically, what you have to remember is that film has broader exposure latitude than video. This means that underexposed and overexposed areas are rendered better on film than on digital media. For instance, on video, a corner of the frame with little light could go completely black, whereas on film is would still show details.
This is important because cinematographers play with light, so a broader exposure latitude medium offers them more opportunity. It's like a painter who has several paint tubes with all the colors of the rainbow (film), as opposed to another painter who only has the primary colors (video). However, needless to say, technology is constantly advancing, and the gap is decreasing.

Why Shoot Video

Video is spreading quickly. As technology evolves, video will soon become the industry standard. It's impossible to know when, but the push towards it has already begun. The main reasons to choose video are (1) workflow, (2) price, and (3) reproducibility.

Workflow

Video can really speed things up. With film, prior to the shoot, someone has to load the magazine in a light-safe area. After the shoot, the film must be developed, processed, and digitized (turned into a digital file in a computer). Film is digitized because most editing are now done in computers, using programs like Avid or Final Cut Pro.
If you shoot video, you can skip these steps. You record straight into an SD card or hard drive. The footage is then unloaded in a computer or separate hard drives. The footage does not need to be processed; you can watch it on the set within seconds after taking it. 

Price

Shooting film is expensive. A 400-foot role of 16mm stock costs about $100. 400 feet of 16mm film is enough for 11 minutes of footage. That means that, when shooting 16mm, you spend $100 for each 11 minutes. But feature films are shot on 35mm, and they shoot way more than just two hours of footage.
With digital filmmaking, the preferred media is SD cards, which in theory can be used endlessly over and over again in different projects.

Reproducibility

Video is also convenient because of its reproducibility. Just like files in your computer, video is digital, so it can be inexpensively copied over and over again without any loss in quality whatsoever.