I have read A Shropshire Lad and most of Moore's Irish Melodies. To compare these is obviously like comparing apples with oranges; but I prefer Moore. Housman is rather bleak and cynical sometimes - one gets the impression that the poet was very unhappy. A Shropshire Lad seems to be without hope.
Moore, on the other hand, is full of spirit; I would much rather reread Moore than Housman, though both are good in their own ways.