I love the shit out of TNG, but those characters aren't timeless. They're trying to be what humans should be instead of what they are, and the milquetoast way they go about it is very much grounded in the 90's.
Are you also saying that you think Kirk is more timeless than Picard? Because if you are, I couldn't disagree more. Stewart is by far the superior actor, and his character is just so much better written. I don't agree with the argument some TOS fans make that the TNG characters are too perfect. If you analyze Picard, he was shown to have his flaws. As a cadet he was arrogant and impulsive, and even years later when he had matured he still had some issues. He had a very difficult time coming to terms with what the Borg did to him. He almost committed mass genocide just out of spite. The point I am getting at is that Picard is a very human character; he makes mistakes and he has his flaws, but nevertheless he has a conscience and stands by his principles, and in my eyes those are some of the main characteristics that make him such an endearing character. Kirk is nowhere near as complex of a character, in part because of the way he was written, and also because of Shatner's overacting.
Moving on, if you ignore Kirk and Picard and analyze the rest of the cast, TNG wins by a long shot. Don't get me wrong, I like Spock quite a bit, and the interplay between him and Bones can be pretty funny, but compared to the likes of Data and Worf they aren't nearly as interesting. Besides, most of the TOS cast just sat around in the background and hardly did anything. They had their moments, yes, but in general they didn't get very much attention and they didn't develop at all. Data, Worf, and Riker and Crusher to a lesser extent, developed a lot during TNG's seven seasons. (Worf would develop even more in DS9).
Frankly, the only reason I believe the TOS cast is so iconic in the eyes of the general public is because they were the first ST cast, but that doesn't mean that they were the best cast to ever be featured on a Trek series.