What are the advantages and disadvantages of these two methods to store your coins?
Well, i think the advantage of using hardware wallet is off-grid, offline wallet, no one would have access to your wallet but you. Also, the exchange wallet has easy accessibility anywhere when you have internet connection but it's less secure compared to hardware wallet. Always remember, not your keys not your coins.
What's clear is that with hardware wallets everything ends up being dumped on you and no one can do anything with what you put there other than yourself and perhaps the family you have given the information to open them.
now everything is advanced and the hardware can easily be used in any system as long as there is an internet connection, so it is clear from a security point of view I totally agree and agree with you, obviously the hardware is very capable to use.