The two approaches to the crisis reflect the different objectives.
The UK policy of the Government buying whole banks was to protect the banks customers (savers and mortgage holders). The plan is that when the storm has passed, the banks can be de-nationalised and sold back to the private sector (possibly even making a profit),
The US is primarily interested in getting the system running again. It has broke down because everyone is scared to trade with everyone else because they do not know how much bad debt is on each others books.
The US plan is to buy these bad debts so everyone can have confidence in each other again and begin to trade again. The US Government will eventually have to try and sell the 'troublesome assets' at a later date. Their concern is save the Corporations rather than protect the man on the street.
The UK Government initially handled the Northern Rock problem very poorly and its solution of nationalising it was one of last resort. Governments should not be running commercial banks, and the sooner they can sell it back the better. However, the result of the the Government buying it, is that the people responsible for its problems were removed and it is now being run by different people.
In the US, the people running the Corporations that made all the mistakes and caused the crisis, are still in their jobs and still running thing, with the US taxpayer picking up the bill.