What are the advantages and disadvantages of these two methods to store your coins?
@mk4 has given you a very precise explanation....if you put your assets on the exchange then it is very vulnerable, many suggest that you use a hardware wallet if you have a lot of assets to avoid the worst that could happen, especially since hackers have 1000 ways to get prey.
When your assets are on exchange, isn't about the hackers because I believed that hackers are not easy to compromise exchange.
I have doubt that the scam that happened on exchange was an inside job and this is what I have worried about when my coin is on an exchange, there is no way to protect us from that scenario. But how about the exchange that offers SAFU? They promised that your fund is safe.
To have peace in your mind, much better to choose a hardware wallet and they are right.
Wont be easy to compromise but the probability or chance would be always there and you shouldnt really cross out into those chances which would really be a regretful thing once it do happen and this is where you do learn up things on unfortunate conditions.
So its neither you would make use of hardware wallet depending or according into your needs so its would really vary honestly.
If you do all sort of security of your account then its what matter most.