But of course there are so many factors going on with crime rates that it's very hard to control just for religion.
There's police presence, functionality of courts, poverty, family stability, gun laws, and of course yes religion and overall culture.
It seems you forgot about one thing: personality. Some people are more troublesome than others and hence more likely to commit a crime. I think it is not enough to consider only external circumstances when explaining someone's behaviour.
I'd say firmly teaching particular ethics in a kid from a young age does that, which can be done with or without religion, ("God will punish you", versus How would that make you feel?", as examples) and it's better to do it without religion, since that encourages greater rationality and critical thinking later on.
Criminals do not always think rationally. Some are simply sadistic, they like harming others for fun. There are also those who like the risk, challenge, the adrenaline rush. Committing a crime is an adventure for them. Not to mention the folks who are thoroughly psychotic.
While there is great room for interpretation of God's commands, lots of room to include the individual religious person's pre-existing morals, sometimes things are pretty clear or at least give a strong leaning in a direction...
People are individuals. They may attach some label, call themselves Christians, Muslims or whatever but their behaviour may vary. Surely, you do not believe that most people just follow blindly their religious leaders, do you? People are more complex than that.