What are the advantages and disadvantages of both ?
The most obvious is that Trezor supports some tokens and Ledger Nano supports a different set of tokens. There's some overlap but there are several well known tokens that are carried by one and not the other.
Trezor has great communication from the developers, they maintain a blog (
https://blog.trezor.io/@satoshilabs) and announce all developments in very real time. They have great explanations on how to do things with their hardware wallet (e.g., claiming hard fork awards).
Ledger Nano is a hardware wallet I'm not as familiar with, so I'll let others preach its benefits or warn about its downfalls.