The model 3 is a great handling car - closest compare is a 2012ish BMW 335xi. It’s heavier and you can feel it in turns, but you can feel the low center of gravity, and the grip/acceleration curve compensates it out. For street use the tires grip and the car overall overpowers its weight. The suspension is good, really reminding me of the BMW. Note suspension is tuned like a BMW with surprisingly similar dampening but overall is not as mature as the 335xi was - on super bumpy roads the tires will stay in contact with the ground but you will feel the difference. The model 3 not going to be close to a Miata, but in its size class it’s a great time. I would totally buy one, and almost did; it always puts a smile on my face.
The model Y is not nearly as maneuverable, but the low center of gravity really helps in turns. It’s better than I expected from a CUV/SUV. Not in the same league as the model 3.
Tesla is really good about test drives - I’d highly recommend it. Even if you never buy one, it’s a solid experience.