Chris asks a good question ("what is the great new tech in the 3?"). I too have seen several people rave about how the 3 is "new" and the S is "old". I am happy to hear examples, but I have a 3 and an S and it seems to me that most of the stuff is either the same, or just making a different trade-off. There are a few things that are better (door pockets, coat hooks), but they seem pretty minor in the overall scheme of what you look at to make buying decisions - and there are plenty of features that go the other way (I listed a bunch of them upthread).
First off, a 2018 S is VERY different than a 2012 S - and in some pretty major ways. We had a 2012 for years and loved it, but we also have newer cars and the differences are obvious. Tesla has been making updates constantly. So calling the S a "6-year-old car" is insufficient to explain the differences.
When it first came out, the 3 did have a notably faster computer. But then they updated it in the S, so that is no longer different (as SigNC noted).
The 3 uses different battery cells. They are a newer design, so some claim they are superior. However, their primary design criteria was a lower price. While they might happen to be better in every respect (longevity, charging speed, temperature sensitivity, max discharge, voltage sag, etc) in addition to being cheaper, I suspect that is not really the case. There has been some promising analysis so far, but there is still much we don't know about them.
The 3 uses different motors. They are a newer design, so some claim they are superior. However, their primary design criteria was better efficiency (to reduce cost of battery required to meet range goals). For some, that is better. But for a lot of Model S owners...well, they are probably more concerned with performance and reliability. Maybe the 3 motor will be at least as good in every other respect...but again, I suspect that is not the case.
Don't get me wrong - I think the 3 is a great car, and in fact I'm replacing my S with one. (Although note that in my case my wife has an X, so most of the S advantages I can still have by borrowing her car). Given the enormous price difference, it is obvious that most buyers will go the same way - I agree that the 3 is a better value than the S. But I think calling the 3 a better car, or even just saying it has better tech because it is newer, doesn't seem justified.
[When I say "better" (unqualified by "value"), I mean in general - not as applied to a specific situation, which varies so much as to be useless for somebody else. When talking about an individual's specific situation I use the wording "better for me". For example, the 3 is better for me given that my wife has an X. However, if my car was our only Tesla, the S would be a better choice for me. "Better" is a complicated word, especially when there are inherent trade-offs to some features like size - it's better when you are putting stuff in it, and worse when you are washing and parking it.]