There is so much more you can do on a pc or Mac on the browser addition than you can on the phone. Examples: you can see how much silver And troops are going to a target with the troop movement screen. You can organize your castles by distance from a target (hugely helpful). You can organize just about everything you need to know... i don't know how people function in this game without using the browser version for what it can do.
One thing I'd like to see from both versions is a way to see how many troops you have total: parked at castles, in transit, attacking, supporting... it's impossible to know what you really have without scrolling through every screen and adding on paper all the numbers. And trying to do that would be an insane waste of time.
Curiously, can't access this forum with a computer browser...