"Perhaps there was more character development than "The Original Series". But I don't believe that "DS9" had more character development than the other Trek series that followed.
To me, one of the simplest (but not easiest!) rules to character development is to see if your characters have fundamentally changed between the first episode and the last. You can certainly make that argument for several Voyager crew: Torres, Paris, famously Seven and the Doctor. But I feel like many characters -- Janeway, Chakotay, Tuvok, and poor Kim -- pretty much maintain themselves throughout the entire run. Janeway will always be the caring and creative leader, Chakotay the careful stoic, Tuvok the pragmatic logician, Kim the panicky newbie. They were consistent in all seven seasons, and while that's not really a bad thing, it also shows a bit of stagnation. Sure, they have their achievements and tragedies, but those things don't really change them on a personal level (the Doctor, though, was always on a quest of fulfillment and growth; Seven kept trying to figure out individuality; if given the chance, Season 6/7 Paris might have slapped Season 1 Paris to get his act together).
I feel like TNG is roughly in the same boat, too. I love TNG as much as the next person, but I'm hard-pressed to think of how someone like Geordi, Troi, or Beverly changed between Seasons 3 and 7. Riker would get his moments but then revert back to his usual self the next week. Data and Picard seemed to get some genuine, gradual growth.
DS9, though, was in another league. Sisko was hesitant about Starfleet *and* being the emissary early on, and by the end of the series he was leading fleets and sacrificed himself for a holy mission. Kira learned to mellow out and trust outsiders. Odo tragically learned more and more about his people until he made the choice to rejoin them once and for all. Bashir went from arrogant hipster youngin to seasoned moral professional. Worf even gained a few levels in badass after TNG. We saw Jake and Nog grow up and mature with our own eyes, with the war taking its toll on the both of them.
But that's not really it. They're the main characters, they're naturally meant to grow. But that DS9 could afford growth for
supporting characters is, where I feel, is strong evidence of more development than any other Trek show. The more we learned about Garak, the more mysterious he became. Rom went from scheming dork to endearing engineer. Dukat kept playing his own game of faux evil/occasional ally until he revealed himself as genuinely maniacal. Damar probably had the biggest change, going from anonymous henchman to major player to heroic martyr.