And that's fine, but I'm not counting the props, sets, and SFX when it comes to the overall story-telling feeling dated. TNG certainly has more modern-looking effects and props than TOS, but I think the overall feel of the stories of TNG are still more dated than TOS.
For example, no one would say that the 1950s film Forbidden Planet has good special effects compared to today's special effects. They may have been good for the 1950s, but not today. However, as a sci-fi film, it holds up extremely well today and its story does not feel dated -- old-fashioned effects and all.
When I watch Forbidden Planet, I don't care what the effects are like. I just get into the story. The same goes for watching TOS today; The TOS effects, sets, and props might be cheesy by today's standards, but I just ignore them and get into the story.
While I generally enjoy TNG, and think TNG's props, sets, and SFX in general are better than TOS, I find it harder to get into a TNG story because of its (as I previously mentioned) "affected preachiness" that often makes me roll my eyes.