Here is a little more information on the Tower & Lyon version. This information came from the 1904 Tower & Lyon catalog reprint.
The wrenches with the short nut were made in 3 sizes of 10 in.,12 in.,and 15 in. The long sleeve nut, i.e. the fluted version, were made in the following 5 sizes, 10 in., 12 in., 15 in.,18 in., and 21 in.
T & L had this to say about "The long sleeve nut": designed and made exclusively by us for our Engineers Wrench, combines two important advantages, viz:--the polygonal section, permitting the application of another wrench when extra power is required, and the parallel fluted section which affords the best possible grip for the hand. They actually show a cut of a SOE wrench that looks to have been expressly made to fit the nut on the wrench to aid in tightening the jaws.
These same wrenches were also made in a version that had a grooved pawl(the moveable part that bears against the pipe) that held a pipe cutting wheel. The pipe cutting version was not made in the 10 in. size.
An explanation was also given for using the "oblique parallel grooves" on the pawl, rather than the more common method of cutting the grooves parallel to the long axis of the pipe. Their logic was that having the grooves at an oblique angle allowed 3 teeth to be in contact at all times, along with giving a more sure grip.
Mike