In contrast to everyone loving the Street Fighter II movie, it is rare to see any love for the Street Fighter Alpha movie. It provides a more complex story, with stronger enemies and inner anxieties taking place, and those are precisely why nobody really likes it.
The problem all lies in the fact that it is an anime based off a video game. When people see any media based off a video game, they expect to see all of their favourite characters with defining moments, and maybe expect a storyline similar to that of the games if they care about that enough. Street Fighter Alpha, however, focuses primarily on Ryu, with Ken and Chun-Li only getting small amounts of screen time and everyone else has minor cameos, and even then there are still characters missing. The storyline, which focuses on Ryu's inner struggles with the Dark Hadou and the appearance of a younger brother he never knew, add a bit more to a character who isn't terribly renowned for having an amazing history or motive, but it means that anyone who would make for a good story are relegated to the sidelines so Ryu can mope about himself.
The sad thing is that the production is really, really good. The visuals are impressive with some excellent background artwork, the music is amazing and gave a great cinematic feel to the movie, and the voice acting is of good quality. The story, however, does not fit with the video game movie standard, and thus why it is hated. Instead of following the Street Fighter II movie's method by essentially making fight scenes and defining moments for all of the characters and then working them into a basic plot, Alpha gets a complex storyline that focuses on one character, adds non-canon characters and makes a major plot point unnecessarily confusing simply by the inclusion of a non-canon character. There are some things where making an uncertain plot point can be good, but when nobody is all that fond of the thing, it just makes them dislike it more. If people liked the movie, whether or not Shun was Ryu's brother could have become a huge point of discussion, but people like neither the movie or Shun himself, so there you go. Also it probably is explained what Shun is, and I'm just not aware. Wouldn't be the first time.
Ultimately, Street Fighter Alpha isn't that bad if you accept that it should be treated as a regular anime movie than one based off a video game, and has a nice selection of extras on the DVD, such as seeing the music being composed, interviews with the director and voice actors and so on, but I'd much rather watch the Street Fighter II movie. It has Dee Jay!