Digital camera: Sony DSC-TX100 or HV9X

The amount of light that can reach the sensor isn't dependent on the focal length of the lens (wide angle/zoom range). It's dependent upon the aperture (although that is dependent on where you are at within your zoom range in most lenses, so the amount of light that can reach the sensor is indirectly related to whatever focal length you are shooting at with any given lens. Lenses that can keep a max constant aperture are called "prime" lenses, but you won't have to worry about that in any point-and-shoot camera). The max aperture at the widest zoom for the TX100V is F3.5 at the minimum 25mm focal length; the max aperture for the HX9V is F3.3 at its minimum focal length of 24mm (the lower the F-stop number, the more light can be let into the lens at that aperture). So the difference there is pretty negligible. Add to that the fact that your max aperture will get smaller the more you zoom in (which is a max of F4.4 on the TX10V0, and a max of F5.9 on the HX9V, which allows less light in), and it's hard to say how that will compare since that max aperture available is dependent on your zoom level being used, and they aren't going to change at the same rate between the two cameras.

Both cameras utilize a sensor that is nearly the exact same dimensions, as well, so that shouldn't play much of a factor amongst image quality between the two.

Hard to say which one I would consider if size and zoom weren't a concern, since those are pretty much the two main reasons to go with one of those cameras over the other. The TX100V has a size advantage with its internally zooming lens, whereas the HX9V's main feature is the massive 16x zoom.

For me, size plays a lot smaller role than feature set, so I'd have to pick up the HX9V to take advantage of that big zoom unless I was really concerned about being able to carry the camera around in my pocket very ofnte. Other features like a maximum exposure time of 30 seconds on the HX9V compared to only 2 seconds on the TX100V would make low light and night time shots (with a tripod or steady shooting surface) a much more feasible venture, too. On the other hand, the TX100V has a nicer viewing screen on it.

Either way, they are two nice cameras, but portability versus zoom versatility is one of your biggest decisions you have to make here.