Hello,
I mean literaly take the city. Obviously the player who gets ''owned'' loses the account on that city and reloads to another of his accounts as many have and the game allows it. Now because there is the money factor, all transactions and drachmas or anything that the defeated player purchased* will transfer to his new account.
Now for the question of improving and the difference of siege/capturing.
Well is another experience having 2 or more cities than one and you can do various things between them. When you siege them you dont take them, the same siege mechanic as we have now. But when you attack to capture it you take it for yourself , with (everything?) new (agreements, academy , ampitheater). I suppose it needs some requirements to take a city or perhaps a new unit to do so.
*will probable be city schema, artisans... around this type of purchases and more, except units.
Thank you for your responses and sorry for my late one.
Archmage