My completely uneducated response:

Woodcock aren't as widely distributed and are harder to hunt with less payoff (lbs per bird) than ducks, so I think duck hunting is probably more popular. Sub gauges with duck engravings do seem a little funny though...

Chapuis and Merkel both engrave woodcocks. I only know that because those two brands are the two I'm considering as my "big" shotgun purchase.

-Leverhead