After tha alarm has been triggered, look closely at the LED as soon as you put the ignition on, this will flash a certain amount of times, corresponding to which circuit has been hit/triggered, listed in the booklet you should have got with it, glass break sensors are notoriously unreliable, especially as yours sounds like adjusted way too sensitive.
The difference in power consumption between this and your old one, did you have a extras such as glass and tilt on your last one ?, these things are very power hungry, had these on alarms that would only last 4 days at most to still start.
Both the tilt and glass sensor are adjustable.
tabetha