What were the design differences between the Leman and Hawken.
Visually they seem much the same.
Fred
What Hungry Horse says is true as far as it goes, but I don't think it addresses the root of your question about the "design differences". To better understand the design difference, it helps to understand more about the background of the principals in the two firms.
Henry Leman was born in Lancaster, PA and apprenticed to Melchior Fordney, a talented Lancaster gunsmith. Leman then went to work for George W. Tryon in Philadelphia as a journeyman gunsmith for a few years, after which he opened his own gun shop back in Lancaster in 1834. Leman was trained and worked in the Lancaster school of gunmaking, except for the few years he spent with Tryon where he probably learned more about building rifles on a large production scale than any particular style.
Even though Leman built a very large number of guns (According to the 1850 census, Leman had 34 employees and produced 5,000 gun barrels and 2,500 complete guns that year) of different types and styles, including NW Trade Guns, the rifles he is most associated with are classic late Lancaster pattern rifles with the triangular shaped butt stock.
The top rifle is an original Leman squirrel rifle that has been cutback to half stock and barrel shortened. The bottom rifle is one of Jack Brook's Leman Indian rifles.
Jacob and Samuel Hawken were born and grew up in Hagerstown, MD and most likely learned gunsmithing from their father Christian Hawken, Sr. They would have learned to build rifles in the style of the Maryland school around Hagerstown. In fact, a rifle of that style survives that is marked "C. & J. HAWKEN", probably built jointly by the father, Christian, and son, Jacob. Another of the same style is marked "S. HAWKEN". Several other rifles exist of the same style that were built by brother, uncles, and cousins of Jacob and Samuel.
Maryland school rifles built by Jacob, Samuel, and Hawken relatives.
Jacob work for several years as a journeyman gunsmith at Harper's Ferry before going to St. Louis around 1818. Samuel arrived in St. Louis in 1822 after having lived and worked in Xenia, Ohio since 1816. Jake and Sam formed their famous partnership in 1825, apparently after the death of Jake's former partner, James Lakenan.
Once in St. Louis, the Hawken brothers were free of the confines of working in an established school as dictated by the market back in Hagerstown, but they still had to satisfy the needs and desires of the customers around St. Louis and points west. A lot has been written over the years about the possible influences that guided the Hawken brothers in the development of their classic mountain rifle. Many have noted the similarities to English sporting rifles as Hungry Horse pointed out. Others point to the Harper's Ferry 1803 and the time that Jake had worked there. Some see a strong influence of southern mountain rifles that were brought by people moving to Missouri from Kentucky and Tennesssee, particularly in Hawken full stock rifles (see picture below). Hanson thought that James Lakenan and guns produced at the Virginia Manufactory had some influence. In reality, all of these probably played some part.
Most peoples' image of a Hawken rifle is the classic S. Hawken plains rifle of the 1850's, but that is the fully evolved late period Hawken rifle. Prior to Jacob's death in 1849, the brothers had made a number of different styles and types of rifles. Based on Charles E. Hanson, Jr's research in the records of fur trade companies, the majority of these may have been full stock rifles.
Unmarked full stock rifle attributed to J&S Hawken
Sublette-Beale J&S Hawken circa 1835-1843
Sporting rifle restocked from HF 1803 parts - Maker unknown
Kit Carson's last Hawken - classic late S. Hawken
If you see any design similarities between some of the Hawken rifles pictured above and the Leman rifles, its probably in the architecture of the butt stock and "Lancaster" triangular shape. I wouldn't place too much significance on this. That shape is what made Lancaster pattern rifles so popular for so long, because it's "pleasing to the eye". By the mid-1800's, a lot gun builders around the country had adopted it. Even lever actions rifles of the later part of the 19th century used that shape of butt stock. It just became the fashion.
Others have posted above about the construction details and differences between Leman and Hawken rifles, so I won't bother to repeat those details.