Here's a tight crop on the Greater Scaup. Now we can see some of the structural traits which are reliable separators of the two species and not, at least normally, subject to much variability. Of course, the wing stripe is useful in telling the two apart but since we can't see that field mark here, we won't worry about it. Note how this bird has a nicely rounded head with little in the way of an obvious peak. If anything, the most obvious angle in the shape of the head is in front of the eye, after the forehead slopes rather steeply up from the bill.
Also note the comparatively massive bill. Big and broad, and appearing thick from top to bottom. It also has a more prominent nail, or hooked tip to the bill. This nail is also blackish, and the dark pigment bleeds onto the adjacent bill, making the entire tip of the bill look dark.Here's a closeup of the comparatively wimpy looking Lesser Scaup. The bulbous head is perched on a rather spindly looking neck, and the shape of the head is distinctly crowned or peaked towards the rear. This essentially gives the look of a tall, domed head while the Greater is low and rounded. The bill is smaller and weaker by comparison, lacking the large, spatulate proportions of the Greater. Note especially the basal portion of the bill on each species - the area where the bill meets the head. It also has a smaller nail at the tip with little in the way of dark pigment, so in this photo it is hard to discern any coloration at the bill tip, while in the above Greater shot it can easily be seen.
That's enough of scaup, I think. If only we could see them this well every time in the field! Thanks to Nonda for sharing this great photograph.