Cloth like diapers do not hold as much before leaking. They don't go well with diaper covers either, as they will make you feel more wet and clammy than you really are. They breathe more too, so they are no good for bowell accidents unless you like making others cringe. The shell of the diaper also tends to stretch a lot, which makes them sag more and need to be refastened more often as well.
Plastic though, tends to rustle and crinkle which some are afraid might make them easy to detect. The good plastic diapers are thicker, and also swell up more too. This can add to the fear of being detected but the added bulk is a trade off for fewer leaks, which actually makes them more discreete. At the same time, this also means they will last much longer before needing to be changed. Thks makes them perfect for overnight use. Though that can be good or bad for the day depending on if or when someone wants to change early.