The first things that come to mind are environmental, lower gravity, and atmospheric composition. Then there are fundamental things like the lack of plate tectonics, and rather than having it's own magnetic field, the moon would be enveloped in the gas giant's field. For perspective the moon is something like the size of a pea or a dime held at arms length, while Jupiter's magnetic field, if visible, would be the size of a basketball held at arms length. Compasses are going to point at the north pole of the parent planet and not the moon. Navigation and technology are going to be hard to develop in such a climate.
Rather than being generally heliocentric, the denizens of the moon will likely have their religion centered around the planet they orbit, likely with divine relationships between their moon, the parent planet, other moons, and the solar body much more distant theologically.