According to the GWT JRE emulation docs (http://code.google.com/webtoolkit/doc/1.6/RefJreEmulation.html) these methods are supported on the Boolean type:
Boolean(boolean), Boolean(String), parseBoolean(String), toString(boolean), valueOf(boolean), valueOf(String), booleanValue(), compareTo(Boolean), equals(Object), hashCode(), toString()
as to the difference between boolean and Boolean object types. Boolean objects can be in 3 states, so it is not exactly the same. But if that makes a difference in GWT (performance wise) I don't have a clue, my guess is that it does not matter much since the GWT compiler will optimize the code and most operations could simply map to native javascript boolean operations.
But as usual: to be certain you must measure (and take into account that this might differ based on what browser/version you are measuring).
The Boolean object type is normally not used very often since the boolean native type is more natural (you don't need to check for null all the time).
