First class and business class are relative terms on a 777. A business class seat is better than a typical airlines first class seat. It is like a normal first class seat on a 737 or 757, but you get to recline a little more, and you get a foot rest. First class on a United 777 is a fully lay flat bed. The most comfortable seat I have ever sat in.
The reason why business is always full, and first usually has 2 or 3 open seats is because frequent fliers often buy coach seats, and upgrade using their frequent flier miles. But you cannot upgrade 2 classes. Works out good in my opinion.