if the game hosted through a server, your connection must be very high and stable. it also take much bandwidth. you also can't play it offline. on the good side, the game only need low specs. it because all process will be done in the server. if you locally install the game on your drive. it need more performance since you're process your game without any external help (server). there are some game that online only but still need to be installed in your drive. it combine the advantage and disadvantage of both.
hope this will answer your question