I don't know what sizes are on your 323i, just from my perspective, there is indeed truth in matching the tire to the desired handling caractéristiques of the car.
On my BMW E90 with the 17" staggered sport setup for summer, I was happiest with the ContiSportContact 3s (non-RFT). Had them once, liked them, then it was a change to Goodyear Pilot F1s which were okay but not as sticky at the limit. The Contis had a firmer sidewall and a firmer ride, but I prefered the at-the-limit feel over the Goodyears, which were very competent but lacked the outright stick when driving 10/10ths. Goodyears had a more comfortable ride, but the roads in NC are good, so not much an issue.
Many years ago, I had the Yokohama S.Drives on my dad's MX-5. A bit soft for my tastes, but perhaps things have changed over the years.
I had the ContiSportContact 5 SSRs on my Mazda3 BM (2014) hatch. A great tire, but it was too much for the chassis and suspension. So while the tires would stick, the body roll was already excessive and had me holding onto the steering wheel for dear life.
I hated the Bridgestone Potenza lineup. On my dad's MX-5 it rode harshly, short lifespan, and let go too suddenly when I pushed it to 10/10ths. Acceptable feedback at the wheel though, I just prefer a more gradual breakaway on my tires (car & moto).
I have the stock Michelin Pilot Sport 4s on my Peugeot 308 GT and it's a great tire. Not a super-sticky sport tire, but that suits the car. After all, I don't have the GTi variant !
I don't really believe in all-season tires. Ton of experience with the ContiProContact (afterthought of a tire, btw. Not even sold in Europe) and it's competent, and nothing else.
