This movie is ALMOST "campy", but it never quite crosses that line. While in most cases, this would be a negative aspect to a film. In "The Crow", it's an essential atmospheric component. This story and these characters only work against a backdrop where reality is slightly bent and cartoonish (like Tim Burton's Gotham City, for example).
The characters are two-dimensional (including the leads), good guy or bad guy, friend or foe, hero or villain, and you know instantly as soon as they come on screen. Again, usually shallow characters aren't good for a movie, but they work here because their only purpose is to move the story forward.
There aren't multiple layers of subtext to unravel here. This is a simple story, stylishly told, about love, friendship, and good's triumph over evil.