Because you have to compare compatible types, since comparing incompatible types for equality will always be false.
String is compatible with Object, so comparing references with those types is not a compile-time error. StringBuilder is compatible with Object, so you can assign a StringBuilder to an Object-typed variable. But String and StringBuilder are not compatible with each other. So if you have a String reference, and an Object reference, you can compare them without a compile-time error. But if you have a String reference and a StringBuilder reference, you can't — the compiler knows that the comparison will never be true.
Note how it's all about the type of the references (the variables), not the type of the objects assigned to them. That's why it's possible to set up your second scenario and have it compile, even though it can never have a true result.
