Advantages against disadvantages...
It hides ur rating, I think this is the only one
Zen mode hides your opponent's nsme, rating, etc so you don't know who you are playing.
A common problem is that people are sometimes intimidated by someone's ratings, so they tend to make blunders, or don't play as well as they would against a lower rated opponent. If you can relate then that's the advantage.
The disadvantage is that you don't know who you are playing, so if you are curious about who you are playing, then Zen mode is not for you
@publius121 can you see it afterwards in your match history?
Yayerz yes you can
Advantages: If your opponent spams you in the chat, you won't see it
Disadvantages: You can't see your opponent's user name and rating, so you might underestimate your opponent's strength
Not seeing your opponent's username and rating means also means you can't overestimate your opponen't strength.
Anything else? Like dragging versus clicking pieces or that is not related.