They do that because there is a lot of Pokémon whose abilities are based on those weathers. Sand Rush (Excadrill), Swift Swim (Kingdra, Ludicolo, Seismitoad, Kabutops) get double Speed if their respective weathers are up (Sandstorm and Rain, respectively). So you can outspeed your opponent and kill opposing Pokemons more faster. Hydration cures any type of status if your on Rain, and more.
If you choose one weather or another, I think its for preference.
Common staple Pokemons for each are:
Sandstorm: Tyranitar, Excadrill, Hippowdon, Tangrowth, etc.
Rain: Politoed, Kabutops, Ludicolo, Omastar, etc.
If there is rain, you don't get the benefits of your sandstorm. So you have to place it again in order to get the upper hand on your opponent. If your sand setter is dead, then your opponent can have a break and place his own weather. Or just relax, because you will no longer outspeed him.