We show that Barkhausen noise in two-dimensional disordered ferromagnets wi
th extended domain walls is characterized by the avalanche size exponent ta
u(s)=1.54 at low disorder. With increasing disorder the characteristic doma
in size is reduced relative to the system size due to nucleation of new dom
ains and a dynamic phase transition occurs to the scaling behavior with tau
(s)=1.30. The exponents decrease at finite driving rate. The results agree
with recently observed behavior in amorphous Metglas and Fe-Co-B ribbons wh
en the applied anisotropic stress is varied.