Just to point out, Kirk spent most of his time in a run-of-the-mill ship exploring the boundaries of known space. Picard spent most of his time rolling around known Federation territory, in the prized Flagship of the Federation, a ship which was explicitly named after James T. Kirk's Enterprise (most Galaxy Class ships are numbered 70000-72000-ish, but Picard's Enterprise is numbered 1701, because Kirk's Enterprise was 1701).
It makes sense that Picard was more about diplomacy and speeches, when Picard's whole mission was about waving the flag and making appearances and motivating people to rally around the Federation. When shit went sideways, Picard racked up a plenty huge bodycount.
Like Kirk, Sisko was out on the frontier, but he was mostly on the station, where things stayed relatively peaceful. Archer was actually the closest to Kirk's role, but not as good. Janeway took things to the extreme by getting tossed out to the Delta Quadrant, and she lost half her crew in the first day, but then the plot armor kicked in and her crew losses pretty much stopped (RIP Lieutenant Carey, the one man besides Tuvix that Janeway didn't give a damn about saving).
This is eye opening. I never really got into DS9 when it aired and I adored TNG. Was not really aware DS9 was as popular
DS9 has a sort of love it or hate it factor, and it's popularity goes up and down depending on where you look. Resetera is one of the places where DS9 is very popular.