When I was in college, and that was over 30 years ago, there was a large series of books in the library authored by a group of sanitary engineers. I cannot tell you what that series was, but it dated from the early 1900's right up into the 1970's. The professionals in this group may know what I am referring to. I do recall reading in one of these books that the washdown bowl such as you describe was deemed unsanitary and no longer made, around 1968 or 9. It was because of the small water spot and the large area of porcelain not covered by water, particular the area in front of the bowl that slopes down to the water thus making the bowl more susceptible to staining. I do recall seeing washdown toilets in hardware stores (Gerber, Sears (which were made by Universal Rundle), and in plumbing shop display windows (Eljer)), but they suddenly disappeared around the late 1960's.
The reverse trap style was also considered more attractive. I recall the Sears catalogue in the 1960’s describing their economy model reverse trap toilet as neater in appearance than ordinary washdown toilets with trap in bulge at front. My response to that is that beauty is in the eye of the beholder, and I do not consider these old treasures to be ugly or ordinary. But that's me.
It is ironic that many of today's bowls have small water spots and large areas of dry surface and they are not deemed unsanitary because they are now required by the powers that be, and for good reasons.
I have four toilets between two residences. Three of the four are of the style that you describe. The fourth is only 2 years old, and for a 1.6, an excellent performer (though it does stain more than my old washdown bowls do).
My personal preference is the older style because for me, they work the best and are trouble free. I am also fond of antiques, and have a small collection of them that I bought in salvage shops and totally cleaned up and rebuilt.
Below are some photos of some action shots as performed by my 1936 Standard MODERNUS in my home and by my oldest, a 1926 Standard TIFFIN in my cabins outside half bath.
In both bowls, you can see the smaller water spot and the sloping surface of dry porcelain.
The newer MODERNUS has the jet at the back of the bowl and a thorough rinse from the rim jets. The flush is fast and complete, every time. This bowl was redesigned later on and the newer design is a bit deeper with a larger water area. But I like the older design better. The only problem with the MODERNUS is that it's easy to stub your toe on its base at the front, and it hurts!!
Lastly, here are some shots of the older TIFFIN. This one has a large jet built into the rim and none at the bottom of the bowl. The bowl also refills from this spout. This bowl later evolved into the Standard EJECTO. I have one made in 1929. It's based on the design of the older TIFFIN (and still has TIFFIN stamped into the back of the bowl), but the spout is gone and replaced with a jet at the bottom of the bowl.
I hope I've helped to answer your question.
achutch
UPDATE 04-08-2015: The bowls marked TIFFIN are actually 2 generations of the "Standard" EJECTO. TIFFIN as stamped on the back of the bowl, tank, and tank lid refers to the plant in Tiffin, Ohio where the fixtures were produced.
ACTION SHOTS: 1936 "Standard" MODERNUS followed by 1926 "Standard" EJECTO