In my neighborhood, we hear false alarms all the time. I think we develop a sixth sense to differentiate between a false alarm and the real thing.
You must consider tactics. First, assuming it's the real thing, tactical advantage lies with the person who remains silent and motionless. Investigate a noise and you're a moving target. Your legal status is stronger indoors than outside your home, where you may have an obligation to retreat if that avenue is available to you.
Also, most jusisdictions do not permit deadly force to be employed in a property crime. If a neighbor's alarm goes off, if they're wired to a security company, then let them manage it. If not, call the police if necessary but don't go out, armed, to investigate. You can be ambushed by the burglar's back-up or lookout and if the police have been summoned by someone else, you don't want to be on the scene with gun in hand when they arrive.
Int'l Assoc. of Law Enforcement Firearms Instructors