What are the advantages and disadvantages of these two methods to store your coins?
Simply put you must never hold your coins at an exchange, now if you are a trader I understand why you have your coins in an exchange, as you are sacrificing some of the security of your coins in order to try to increase the size of your holdings.
But if you are not a trader then your coins must never be in an exchange or any wallet you do not have the private keys, having your coins in a hardware wallet gives you complete ownership of your coins while at the same time it gives you protection from hackers that most people cannot get on their own, so if you have to decide between those two options then get a hardware wallet, I know they cost money but they are worth it.
By understanding the explanation you mentioned above, I think it is a knowledge for all of us, that storing assets on an exchange is more risky, because even the largest exchanges have experienced hacking, therefore hardware is a wise choice where the responsibility for security lies with yourself. and finally we should understand the signs that a hack is about to occur, so that we can prevent it