This thread reminds me of Walker Evans' work depicting the streets of New York and the southern U.S. But, I think that Evans' work is deeper than Parr's in a number of ways. Evans' use of irony, for example, is resonant and meaningful, while Parr's is (to me) more superficial. If I think of, for example, Evans's picture of the woman wearing stripes standing in the door of the barbershop; this picture reveals an ironic (even sardonic) attitude about the woman's dress and the gauche paintjob of the scene and could be linked to various themes about the decay of the south, the reluctance of the south to morph into the prevailing American culture of the time, etc.
However, Evans manages to somehow (and I wish I knew how to do this myself) remove the subject itself (i.e. the woman and her position in the doorway) from the picture so that the combination of those elements form a complete and meaningful photographic whole. While I see irony in the Parr picture above similar to that in the Evans work, I don't perceive the same level of "desubjectification" necessary to transport the picture from snapshot to something more (and I'm not knocking snapshots here at all). I think Atget could be compared to Parr in a similar fashion as well.