A currency controlled by a single individual, company or government would not need to work like Bitcoin. It would be centralised - there would be no need for mining, running special clients and so forth. Those are only a key feature of some decentralised internet currencies similar to Bitcoin.
It is possible that such a currency would replace Bitcoin, but it would be done most likely by law and force, rather than because of its benefits. A currency like that might exist alongside Bitcoin, but how much it is used would depend on the appeal and use of it. Should it for example be the only currency you could pay taxes in, it might as well exist for a long time.
There is also an idea of Digital Coin, where many such currencies might exist at the same time because they would be beneficial for the companies and their customers. It has space for Bitcoin-like currency - as a measurement of standard of value, as well as last resort for trading.
All in all, Bitcoin won't probably be replaced, it might be outlawed, and other currencies might exist alongside it.