Hello Brian,

There was a very serious debate about the same issue with the "first" record of Wilson for Egypt at Egyptbirdgroup, where two pictures were available and we couldnt decided over, personally I opted for Marsh finally, but it was more a overall impression for me than a positive ID at the end.

Anyway, I digged out some of the IDs what I can copy here:

A summary for Wilson was:
1.  A solid Dark over the ear converts and tucking in just under the eye,on Marsh this would show as more intricate markings,even though this has been sharpened & had a lot of digital noise in the shot,it still would not show such a solid mass. This dark ear covert is part of the curving dark side of neck marking, ( 2 ) that Wilson's show, especially in adult summer Wilson's & to a lesser extent in winter Wilson`s and Marsh don't to this extent.
3. The bill has that ` being stretched look` off its face where upon Marsh does not show this look.
4. Plain back typical to Wilson's,where on Marsh the feathers have fine markings across its back feathers. Even though this photo has its digital noise,it would not show like this on Marsh and i would expect to look darker across its back.
5. The legs are very  angulated ,typical to some US waders they have this top heavy look caused by the tibia being shorter. In adult summer Wilson`s the legs are black but in the winter they turn to a yellow colour. A gradual change in colour and the dark mud smeared over the legs would give these legs this look. 

Another summary for Marsh was:
1) bill, which is stronger than Wilson’s, with an heavy first half and a slightly upturned end, really like a mini-nebularia. Wilson’s never seem to show such an heavy bill 2) legs, a very long tibia and 3) the real clincher seems to be the shape of the bill base and nostrils: in Wilson’s, the top of the upper mandible reaches the forehead at the level of the inner end of the gape nearly, creating an concave edge of the upper mandible; in Marsh, the edge of the upper mandible is straight and extends outward, as the bill reaches the forehead much forward compared with gape. 3) the nostril which are wide and large, such that you can see through, whereas nostrils of wilson’s much narrower.
 
Hope it helps,

Cheers, Lajos