What are the advantages and disadvantages of both ?
I personally use Ledger Nano so I can vouch for it. It will allow you to store several altcoins along with your Bitcoin which is handy when you are keeping everything in one device.
Here you will find the list of supported coins for ledger neno:
https://www.ledgerwallet.com/cryptocurrenciesSorry for my ignorance on Trezor I really do not know much about it