Look, plenty of crimes have been caught on tape by the surveillance camera, so I don't think even real cameras will necessarily stop a robber. To get anywhere, it seems like we need some sort of statistical study that can never be done. We need to survey criminals and find out how they respond to each form of deterrence. Without that, we are just left with anecdotal evidence. My neighbor was robbed in spite of fake cameras. My neigh has fake cameras, and he's never been robbed. My neighbor decided to confront the two men robbing his house, and he was badly beaten up. This guy I know confronted the two men invading his house, and beat the crap out of them. (This is a true story -- the criminals followed his wife home and broke in in the middle of the night.)
Are we making home security decisions based on fear and fearful or impractical thinking? Or are we using evidence and fact? So much of this seems to depend on what we know/expect from the "opposing team," the robbers/burglars.
I like what Nurse Mike has to say.