normal maps render faster than bump maps. because for normal maps the slope of the normal texture are already calculated; bumpmaps needs to be analyzed at rendertime and calculate the slope.
thats why games use them most. they are realtime/pre calculated.
again like you posted, norma maps take into account lighting info. so it s more realistic than a bump, which is just flat, regadless of light direction.
and also the fact that you can bake a lot of surface info into a a normal map, u can bake something low rez look really great, or a medium rez look like its a high rez mesh, or just use it on a high rez for low frequency details that a displacement map would take too long to compute.
i stopped using bumps maps completely just because its faster and maya can render them without problems.