> The British version can be much bleaker.

I think this one is a miss. TOS is inspired by _british_ naval history. Loss, fear, and failure are central to the show. In this era of TV, leading characters still had large flaws. Kirk is frozen by choice, Spock believes himself superior, Bones is a bigoted luddite. We as viewers get to see the pain this causes and their efforts to improve. It's wholly different than modern US television including all other ST media. Meanwhile, 70s Dr. Who is packed with automatic weapons fire and explosions and the formula has always been the Doctor knows best. (I am a huge fan of all the mentioned shows.)

For a good, modern example we can look at Ghosts (suddenly renamed "Ghosts UK" on my streaming services) and Ghosts US. The adaptation is agonizing. They stripped the important aspects of the story but kept a boy scout, toy soldier, and an interracial marriage. I found that telling.