Answer
The tread design in car B yields a larger $\mu_s$ than that in car A.
Work Step by Step
In an unbanked curve, static friction $f_s$ provides the centripetal force to keep the car successfully negotiating the turn. So when a car cannot make a turn, that means $f_s^{max}$ does not give enough centripetal force to keep the car on track.
In this case, car A cannot make the turn while car B can. This fact tells us that $f_s^{max}$ of car B is greater than $f_s^{max}$ of car A. And since $$f_s^{max}=\mu_sF_N$$ and 2 cars have the same $F_N$, we conclude that $\mu_s$ of car B's tires is greater than car A's tires.
