From a naval architecture perspective, these vessels are interesting, IMHO more so than their ocean counterparts of the 1812 period. The men that built these ships were faced with two major problems; the need for shoal draft vessels, and the need to build them quickly.
Shoal Draft: Lakes Champlain and Erie are both studded with sandbars and overall Erie is the shallowest of the five Great Lakes. For service on these lakes, shallow draft vessels were required. To be effective warships, ability to carry heavy armament was necessary. On the other hand it was not necessary to devote internal volume to carry fresh water. These requirements would dictate a wide hull with minimum draft compared to their salt water cousins. Draft is also related to transverse stability. The wide hull form would help to allow the ship to carry her armament while under sail.
Building Shortcuts: For Eagle, the Browns eliminated knees by sandwiching the ends of her deck beams between a pair of heavy longitudinal clamps. Famously Noah supposedly said that “construction only needed to be good enough for one battle.” Not said was that neither lakes Champion or Erie would produce the long rolling waves that would twist hulls like those on the oceans. The heavy longitudinal clamps would also add longitudinal strength.
Roger