A reasonable index of the turn-of-the-century top shotguns, would be what guns were the "Top Guns" using?
Prior to 1895 clearly British - mostly Greener and Scott
After Fred Gilbert won the First DuPont Grand Smokeless Championship Handicap Live-bird Tournament October 1895 with a Smith, the Smith was most popular.
Guns used
https://digital.la84.org/digital/collection/p17103coll17/id/53099 About 1899 (Gilbert switched to Parker that year) Parker took over (with increasing popularity of Winchester 1897 also).
25s at 1901 GAH at Live Birds and the guns used
https://digital.la84.org/digital/collection/p17103coll2/id/42076
Smith went 1-2-3 at the 1902 GAH at Live Birds (Last)
https://digital.la84.org/digital/collection/p17103coll17/id/41019 Lots more here
https://docs.google.com/document/d/1D8QkBDo-KIQYk2G8lkE-kHLUybB5NJzBahX_eFKEyuY/preview 
