I agree that the .500's, with their light bullets were insufficient for the larger species. The .577BPE with the 650gr. bullets were much better in this regard.
Here in NA, the Winchester lever actions, specifically the model 76 in either of the .45 cals or the .50/95 were sneered at by the buffalo hunters as being inadequate for bison due to their light weight bullets. (according to Frank Sellers book on the Sharps rifles)