LC Smith is a case study in how things can devolve over time. I'll spare you the history lesson (although it is a very interesting story) but simply put, it all started in Syracuse, New York with a small maker who largely hand-made very effectively designed shotguns. They were initially funded (& named) by Lyman C. Smith, a larger-than-life industrialist (who went on to build his own skyscraper in Seattle). Another big New York industrialist family, the Hunter Brothers, bought the original company from Mr. Smith (Lyman's next big adventure was building typewriters, ever hear of Smith-Corona?) they then moved the entire gunmaking operation to Fulton, New York. In Fulton, the Hunters (essentially 5 brothers who got a job in a company bought by their father) set about to scale-up (modify) the original LC Smith shotgun design to better facilitate mass-production. It took them about 25-years but Hunter Arms finally "succeeded", eventually ramping-up production to churn out about a half a million guns. The earlier products (from Syracuse) were essentially works of art, with even the entry level guns (Quality 2) being very well finished, the last guns (in the 1940s) were cheapened to the point where they barely resembled the original design. Pre-1913, Smith guns were still well made (w/lots of hand-assembly & finishing), post 1913...well, it became something of a crapshoot after that. Higher-end guns could still be quite artfully executed, but the vast majority were bottom-end guns (i.e., the "Field Grades") and they got progressively less well-made over time. They switched from English walnut stocks to American walnut around then and the infamous stock cracking problems became more pronounced.
If yours is an "O" grade gun then it's pre-1913 and should be a fairly decent firearm. It's a sidelock while your Parkers are boxlock guns so... there are some differences in geometry. But the rest of it is mostly just advertising (Elsies are the crudest of the sidelock designs when compared to the British versions). I "rediscovered" Elsie a few years ago (my first double was an inherited Elsie Field Grade) and I've thoroughly enjoyed the education (& the history lesson).
A 1940s gun as compared to an 1891 gun.
A 1st year Fulton gun (1890), made from actions & wood supplied by the earlier Syracuse operation. Compare it to the 1940s gun above.