Hi Diana, these are two of the top cameras in their class. The Canon SX40 gets higher reviews at amazon.com, so you might consider that a reason to go for the Canon vs the Fujifilm, but I think you'd be happy with either.
What camera do you already have? The main reason to get one of these cameras is for the incredible huge zoom. 30x zoom is really a lot of zoom, more than you'll probably ever need. You might consider a travel zoom camera, with say 20x zoom, which is still more than enough for all types of photography, and will be much smaller.
I get the sense that these cameras don't work that well at extreme zooms, and that manufacturers are going a bit overboard.
One last thing to consider is that almost all cameras (except DSLRs and Mirrorless) have the same small sensors, and are going to get similar image quality especially in low light. If low light is important to you, you might want to consider what we call a pro-digicam such as the Canon S100, they typically have little zoom though.
IT sounds lk something between a travel zoom and a prodigicam would be perfect. I was indeed wondering if it truly made a difference having such a huge zoom. I would be willing to compromise and getting something less than 30 but with good low light. I did a search on prodigicams but they all seem to have very low zooms, while travel zooms seem not to have good low light capabilities.
1)At what range/number will a zoom start delivering good pictures? meaning, how low can I go and still get good results?
2)What range/number should be the minimum I should look for as far as Low Light is concerned?
1. I think 20x zoom is a huge amount of zoom, and will work great for every scenario.
As you use more zoom there are two factors that work against you: lenses receive less light the more they zoom (the aperture gets smaller), and camera-shake movements are magnified more. Also focusing is harder with less light. The result is that you get blurry photos if its not perfect conditions, so using 35x zoom will be hard unless its a perfectly sunny day and your subject is not moving.
2. Low light is one of the hardest challenges in photography. To do it well you need a large sensor, and a fast lens (wide aperture).
To do this well I'd actually recommend an APS-C sized sensor (mostly found in DSLRs and mirrorless cameras) and a f/1.8 lens.
So, thats not a great answer, but the pro-digicams are the closest you'll get to that in a small body.
It will probably be an improvement in low light over what you've got, but nothing ground breaking.