Point and shoot cameras typically last a few hours when running on batteries. Trail cameras typically last a few months to a year because they enter a low-power sleep mode between photos. The endurance varies a lot among brands and models, in part because some have deeper sleep modes than others. There is also two orders of magnitude difference among camera models in the power required to take a single photo.
So the answer to this question depends on what camera you use. If you have a camera with a hungry sleep mode, it will run the batteries down quickly regardless of how often photos are taken. If your camera has a deep sleep mode, it will last much longer if fewer photos are taken.
If nighttime photos are taken, 10% to 40% more power is used to illuminate the flash or infrared lamps. Motion detection probably uses more power than timelapse.
If you are taking one photo every hour, a typical battery life could be 4 months to a year or more. More frequent photo capture will shorten battery life by an amount that depends on the camera and how it is used.
There are some relevant data here, although it is not clear how reliable they are or how to interpret them.