I currently own a S100D and Model 3 with LR and PUP. The Model 3 definitely has a tighter turn radius. It's simply a smaller car. It's relatively lightweight and maneuverability is it's number one strength compared to the S.
I think one big thing many Model 3 reviewers aren't clarifying when they're saying the "Model 3 is better than the Model S" is what year/iteration they have. I think most of the reviews have been comparing the Model 3 to a 5 year old Model S for example which is very different than a current year model S.
I think the Model S is better looking, the air suspension is better than the standard 3 suspension, feels more luxurious (e.g. presenting door handles, motorized hatch, etc.), better glass roof, the current gen seats are better, it's much bigger, and it's quite a bit faster.
There are some other things I commend the Model 3 on including the screen processing speed and placement, turn signal stalk operation, headlight road illumination, and a big one is battery efficiency. Ballpark I think the model 3 is about 20% more efficient as kWh per mile from what i've been observing. I believe this is largely in part due to the significant weight difference and possibly due to more efficient battery tech/cells. I also really like the phone as key function.
Dollar for dollar the Model 3 is definitely a better value, but if you want the extra space, speed, luxury then you simply can't put a price on those wants or absolute needs.
Bottom line:
There is no better luxury sedan out right now than the Model S, and there is no better mid-size car out than the Model 3.