We consider the Thomson and Compton scattering of high-energy electrons n an intense laser pulse. Our simulations show that energy losses due o radiation reaction cause the emitted radiation to be spread over a roader angular range than the case without these losses included. We xplain this in terms of the effect of these energy losses on the article dynamics. Finally, at ultra-high intensities, i.e. fields with dimensionless parameter a(0)similar to 200, the energy of the ission pectrum is significantly reduced by radiation reaction and also the lassical and QED results begin to differ. This is found to be due to he classical theory overestimating the energy loss of the electrons. uch findings are relevant to radiation source development involving e ext generation of high-intensity laser facilities.