And maybe TOS was best because its three leads were archetypes; you had the brave and adventurous Horatio Hornblower figure in Kirk, you have the cold intellectual in the form of Spock, and you have the emotional and moralistic McCoy. Though the casting was never quite that intentional, it's pretty clear that by the first few first season scripts were being produced that Roddenberry and his writers understood the good fortune they had in the chemistry between Shatner, Nimoy and Kelley, and fleshed out those three characters to a point that by the mid-way point of the first season, we basically have the Holy Trinity in place. Thus, when you have the penultimate scene in The City On The Edge Of Forever, where McCoy is restrained from saving Edith Keeler, you have those three archetypal characters in one of the entire franchise's most dramatic moments.
And that really is the magic of TOS; some damned good stories matched up with actors with incredibly good chemistry (which is something you can't manufacture, but was just damned good luck on Roddenberry's part), and the rest just flows. Even awful episodes are redeemed by the fact that Kirk, Spock and McCoy are in it.
You can see through the other Star Trek series where the writers and producers tried desperately to reproduce that chemistry, but even when they came closest in the final seasons of TNG, it still felt somewhat stilted, as if the actors and writers were trying to show us what good friends they all were, without ever really convincing us emotionally that these people were more than just comrades. I suppose the friendship between Geordi and Data came closest, but even that felt one-dimensional as opposed to what seemed like genuine love and friendship between the three TOS leads.
And the brilliance of the TOS characters extends even past the three leads. The second tier characters; Scotty, Uruha, Sulu and Chekhov all were well enough written and portrayed (more the latter than the former considering how few lines these actors generally got) that you could feel some emotional attachment to them. Scotty, in particular, is one of my favorite characters out of the whole ST universe. A bit cranky, but brilliant and incredibly competent, he's sort of the archetypal engineer, to the point where I've read that a lot of people were inspired into technical fields because of Jimmy Doohan's portrayal.