We have Lesser Kudu on Tumaren but we have only seen Greater Kudu on some of the nearby hills (recorded less than .5kms away). It is likely that Greater Kudu have crossed Tumaren as well but we have not yet seen them. On a recent trip I took the following picture of a Greater downstream on the Ewaso Nyiro River and then The Lesser I took a few kilometers from Tumaren. Seeing these images together is nice because you can more easily see the differences than you might in some guide books. The first image is the Greater. Males have a pronounced dewlap, they are generally large and bulky, have an even and overall greyer coloration, and lack the more striking white markings that the greater has on his neck.
And here is the Lesser. He is a smaller with more dramatic coloration. Lesser often are said to have more stripes but this characteristic is not needed for ID. Habitat is usually the best way to narrow it down quickly, Lesser preferring flatter dryer, hotter places while greater prefer more rugged hillside type habitat.