My dad briefly had a MYP and I have an M3P. For how similar the cars should be on paper, the truth couldn't be any further apart. The 3 legitimately handles well. It's no BMW M3, but if you generally like the feel of the German sport sedans, you won't feel too far from home in the model 3. I do wish Tesla had a performance tier that came with a greater degree of suspension enhancements (stiffer bushings, ball joints where appropriate, more aggressive alignment, that sorta thing), but that's just not their MO.
The suspension on the Y on the other hand just could not keep the body in control whether accelerating, turning, or braking. I felt like I was constantly fighting the car. Someone earlier brought up a 3-series vs X3, but it's not really the same. The X3 can still legitimately drive well. Not 3-series level, but it doesn't feel like it has broken suspension either.