Let's say that a gas giant (around the same size and distance from the sun as Jupiter) has a moon that supports life. The moon is around the size of Mercury (if this is too large please let me know). Would the star be bright (or even large) enough to be considered the difference between day and night, or would the gas giant's reflection of the star be considered the 'sun'?
First of all, the moon will always get weekly blackouts once every few years in an eclipse. Making the likelihood of a liveable moon much less likely (or at least one not using artificial light and mass weather controlling, but once you use this the practical side of this question sort of goes down the drain).
Second, the gas giants in our solar system (including Jupiter) all absorb the light particles that hit them. The little reflection is dark blue or ultraviolet in some cases, which won't help brightening the planet.
Third, the light reflecting off the gas giant will have to travel a further distance to get to the moon. Plus the gas giant will absorb huge amounts of the light and the reflection will be less powerful.
Forth, since Jupiter and it's moons are so far away from the sun, the moon will get little light from either. To make it habitable you will need artificial light e.t.c. A way to avoid this would be to make this universe of yours have a much bigger sun. The problem with that would be Jupiter's light would then become nuisance not a helper. But because of the things I said earlier I think the light from the gas giant will be insignificant to day to day life. What will change from the gas giant will be things like the tides.
As a rule, the reflection of light from any source is never as intense as the light coming directly from the source (unless we are talking about concave mirrors here, which we are not). Furthermore, it is not known what is the composition of the gas giant's atmosphere. Some gases retain heat better than others. Although all of the gas giants discovered so far has an atmosphere composed mainly of hydrogen and helium, but if the gas giant in question has its atmosphere made of greenhouse gases ... (don't take that seriously, the chances of this happening are nil).
Gas giants, the size of Jupiter generate more heat in their cores than they get from sun, so if the planet has a calm atmosphere (it's like a joke, expecting a gas giant to be calm) then there are good chances it could provide the planet with some balmy warmth. More so if the atmosphere of the moon has a good ratio of greenhouse gases.