Always wonder when woodcock are discussed.Is it the"American Woodcock"- Philohela minor ,or the "common snipe"-Capella gallinago.Different species,but somewhat similar to many observers.They are of the same family-Scolopacidae.
Given their differing preferences in food and feeding, habitat, cover, concealment, holding and flushing behavior.......
For the reasons Dave mentioned, I see them as two very different birds to shoot - although they do look alike. Funny story to 'illustrate' the confusion though;
I was talking to a buddy in Louisiana about shooting woodcock on his duck lease last year. We talked many times and finally arranged dates. I was really excited! A couple days before I traveled he sent me an email that basically said, "Oh, by the way, we call 'em snipe down here, not woodcock." Another phone call cleared up the confusion - shooting in the thin cover of cow pasture, just off the duck swamps - we were definitely shooting snipe, not woodcock.
Having said that, snipe are also great birds to test your patience and skill with a gun.
I think snipe are best cooked like chicken mcnuggets - deep fried with a tasty little batter. They make a great appetizer. Woodcock breasts in a wonderful homemade mushroom soup served over quinoa is one of my favorite meals.