I assume by low light shots, you mean without flash.
If you use a tripod to support the camera and don't take any pictures where there is subject movement, both cameras can do a good job.
But if you want to "hand-hold" the camera or have any type of action in the photo, neither camera is a good choice.
The Achilles heel of the small digital camera is low light performance.
Low light means that you have to use high ISO settings if you have any camera or subject motion. The small cameras will let you use high ISO settings but you also get high noise levels with the high ISO settings.
This makes you pictures look grainy and dull.
To get good low light photos with a small camera, you need flash or a tripod.
A camera that can do well in low light (without flash) will cost you close to $1,000.
I'm going to buy a digital camera. I don't know much about digital cameras but would like to get started. I will be taking a lot of low light photos indoors and night shots. I'm looking to spend 300.00 or less. I might go higher if I find something I really like. I've been looking at the fuji finepix s1500fd and the canon powershot sx 110 is. Your thoughts on these cameras or any other suggestions are appreciated.