I previously had a Model S, 90D (Not a P) and now have P3D. I'm not saying it is an apples to apples comparison, but in reality most of my driving is typical commuting.
That being said, overall, I am much happier with the Model 3. Mostly, it comes down to what you get for your money. You are getting all of the benefits of a Tesla with a much lower price tag. Sure, a Model S Performance variant can beat it off of the line, but at least for me, how often does that really matter?
What I do miss from my Model S? The trunk hatch and the heated steering wheel. I don't even miss the 2nd display. I thought I would, but I don't. If you need to haul a big box, the hatch on the Model S was amazing. It really allowed for some big cargo to be loaded into it. I also miss the wiper stalk on the Model S. The Model 3 auto wipers are changing all of the time, sometimes an update has it too aggressive, then it patches and it isn't aggressive enough. It is close though. The "always on" power that I had in the S was also a plus, which allowed for things like easy Dashcam installs (while parked) and phone charging when the car was off.
The big thing though is what I pay. My monthly payment is less by a significant amount, and my insurance payment is less by a significant amount. For the cost difference, I don't feel like I have lost anything. Sure, I miss those small things about the Model S, but I also feel like I have gained things in the Model 3. It feels much more nimble when driving and the computer is much more responsive. The autopilot is much improved than my old S. The stereo (and sub) sounds better to me and the seats fit my body better. It's plenty fast and turns more heads. The tech and the car are brand new, and having a warranty on a Tesla is a big plus. (Parts and repair bills are no joke)
My wife has a Model X, and that is a totally different car. I think it compliments the Model 3 very well.