I very much appreciate not having to log in Tana in my browser several times a day. That was an irritating barrier to entry. My pattern of use is to look into Tana only occasionally.
The app version of Tana is better looking - it's bigger on my screen and easier to see.
The side menu is easier for me to read than the tab menu.
The tab menu can be harder to pick out from the other horizontal strips of text at the top of the interface.
The side menu takes up more horizontal room, which can be a problem occasionally.