Well, strange question because it is in fact both.
To some degree it depends on for whom you are talking about.
For the director, who has the artistic vision of what the movie
is about, and how it should look, etc, is is typically an art. For
him, the business side of things is often a real drag, something
that just gets in the way of the "art", or the film. This can be
true of lots of other people involved in the film, too, such as the
DP, the actors, special effects, etc., etc.
For the producers, the studio execs, the UPM, and other folks
with similar concerns and job descriptions, it is really more of a
big business. They do not think about the film in terms of "Will it
be artistically significant?" but rather "Will it be financially
successful?" To this degree many of the "artistic touches" in a
film can be seen by these people as unnecessary, or even
detrimental to the bottom line.
So you can see that film making is not only both an art and a
big business, but that in fact art and business coexist and even
conflict simultaneously in the world of film.
