Comparing equally out-of-the-money calls and puts

In a Black-Scholes world, compare a call struck $10\%$ above the current stock price with a put struck $10\%$ below it (same expiry). Which is worth more?

The call. The lognormal distribution is right-skewed, so a $10\%$ rise is more likely than reaching $10\%$ down in the measure that matters, and a positive rate also raises the forward toward the call strike. For example, with $S = 100$, $\sigma = 20\%$, $T = 1$, $r = 0$ the call is about $4.29$ and the put about $3.59$.