Power and resolution. With each turn of the stepper, screws move the carriage 8mm and GT3 pulleys/belts move 60mm. So when you break that down into fractions of motor steps there is a much finer resolution with screws. Screws also have better mechanical advantage and thus offer more power. From the other side however, belts offer more speed which is fine with softer materials. Which to go with is largely determined by what material you are cutting and what resolution you require. For aluminum
Sorry, I just read the new post listing and didn't notice what section this was under. But the same applies. Belts offer speed at the expense of resolution. They also offer more configuration possibilities.
