Electronic structures and optical gains of bulk GaN and GaN/AlGaN quantum wells (QWs) are theoretically investigated for the wurtzite and the zincblende structures, using the k.p theory. It is found that the lower crystal symmetry, that is the wurtzite, is preferable for the lower threshold carrier density in the bulk. Although the QW structure leads to symmetry lowering only in the zincblende, we can not find a significant benefit of the zincblende QWs. As for the reduction of the threshold carrier density, biaxial strains are more effective in the zincblende. However, the threshold carrier density is still higher than in the wurtzite. It is proposed that the uniaxial strain in the c-plane of the wurtzite is more useful for reducing it.