The main advantage that zippers have over buttons is one of function. The zipper is more efficient to use. The use of buttons require more motor skill to close, in addition to adding bulk to a garment. The disadvantage of zippers is the fact that they are more likely to break. get stuck, and are much more difficult to repair.
Some things work better with zippers, and others with buttons. Also, some things look better with zippers and some with buttons. I think it depends on what you are using them for when deciding which are more useful. A blouse generally looks better and is probably more comfortable with buttons, while a jacket generally keeps you warmer when it has a zipper.
Unlike zippers, button flies are not very firmly fastened onto the jeans. It is therefore a very common occurrence to find buttons actually falling off the rows leaving you completely helpless and embarrassed. Finally, button fly fastening on jeans is very more difficult to work with. This applies whether or not the jeans fit properly. You will have to spend time fastening each button and ensuring that it is set nicely enough every time, which is extremely inconvenient if you are in urine emergency.
Buttons are more useful than zippers because buttons do not get stuck as often. When a zipper breaks, it's difficult to replace. Most people can sew on a button. Buttons are also more colorful and varied. They offer more options for decoration and design in the fashion industry, so they are more versatile in general.