The immigration law does a plethora of things such as making aliens 14 years or older who are in the country for longer than 30 days to have their registration documents in their possession at all times, but the biggest addendum to it would be the fact they can check for a persons documents at all times during a lawful stop, detention, or arrest. This means they can increase the punishment if someone is already under arrest and doesn't have legal documents reducing crime, albeit in a very brute forced fashion.
The Arizona illegal immigration law will not stop or reduce crime. If anything there is the potential for it to cause more crime from protests and those upset with the law. This is not to say the law is not good or needed, it just won't stop or reduce crime.