it is sometimes said that a burglar walking down a road will look at the houses and choose the one that looks easiest.
So an open window, a front door with just a Yale lock, a ladder left helpfully at the side of the house, car keys close to the letterbox, will all attract her more than the neighbours' more secure home.
It follows that if your neighbour (appears to) have a modern alarm system that is turned on, and yours doesn't, your house will seem the easier of the two.
it is also sometimes said that the greatest deterrent effect of an alarm is a visible bell-box on the front and the back of the house. Many boxes now have little flashing lights to make them more prominent.
Burglars will also know that if a front or back door, or garage, is open, then the alarm is probably not set. Only the cheaper DIY alarms, AFAIK, will set if a protected door is open.
Round my way most burglaries seem to be carried out by teenage crack-heads, who have no understanding of alarms or locks, and will just lob a brick through a window and run away if an alarm sounds. They are particularly fond of tools left unattended, and garden sheds.