David, these are both enticing sabers, and well worthy of being stabilized with conservative restoration (I always hate overcleaning....an old salt like me relates to patination)
I've been plowing through stuff here in the bookmobile but at the same time getting ready for another departure northward. In Wagner ("Cut and Thrust Weapons" Prague, 1967) I did find, as suspected, an Austrian parallel to the lionhead. On page 434, plate 64, this same basic style is seen on the sabre of a senior noncommissioned officer in the 'Prima Plana' infantry with the years 1776-1777.
In the case of the sabre illustrated in Wagner however, the hilt is in brass and has a knucklegard, and the quillon extends straight out (as on French military sabres). The ecusson/langet on the crossguard is this same rounded diamond shape, and is profiled.
While it is not a perfect match, it is the same lionhead form with capstan on pommel, the same langet form and similar grip type. This of course suggests the Continental provenance of the sabre and that your sabre is 'of the type' and probably produced in period or subsequently within reasonable time, but for other issue.
Is there evidence that a knuckleguard was present, as should be on these type hilts? The quillon is curiously pointed downward with no terminal, is it broken off? The metal is dull gray, can you tell what material?
As for the other sabre, still no match, but as previously noted, these type pommels are known to have been on French sabres which usually carried neoclassic themes in motif. The United States typically followed French fashions in military uniform and weaponry post-Revolutionary War but in larger degree at the opening of the 19th century (Federal Period).
In this sabre the pommel is of similar form to the officers swords later in the century, and the fluted grips also. French sword grips often had vertical fluting but ebony was much more common. The interesting vertically sectioned langet seems to suggest U.S. as well as the notably parabolically curved blade. These strong curves were much favored on some of the earlier U.S. sabres, particularly those made by the Virginia Manufactory. Many of these early sabres were incredibly long with dramatic curve, and most were shortened down by Confederate officers during the 'War Between the States' (Civil War) as I was told vehemently to call it when I lived in Nashville!
There is nothing comparable in "The American Sword" (H.L.Peterson) but I just noticed Fernando's astute comment....the material in the grip does indeed appear 'organic' and when cleaned...ebony? If so, this is French I would think.
As always.....more research to be done
All the best,
Jim