Answer
The chance of the light car and heavy car safely rounding the curve is the same.
Work Step by Step
In an unbanked curve, static friction provides the centripetal force stopping the car from sliding. We have $$F_c=f_s^{max}=\mu_sF_N$$
Assume there is no vertical acceleration, so that $F_N=mg$ $$F_c=\mu_smg$$
On the other hand, $F_c$ equals $\frac{mv^2}{r}$, so $$\frac{mv^2}{r}=\mu_smg$$ $$\frac{v^2}{r}=\mu_sg$$
It can be seen here that the risk of sliding in an unbanked curve does not depend on the car's mass, so all things being equal, the chance of the light car and heavy car safely rounding the curve is the same.
