How Does the Shape of the Volatility Curve Influence the Theta of OTM Options?

If the volatility curve exhibits a steep skew (OTM puts are much more expensive than OTM calls), the theta of the more expensive OTM options (e.g. OTM puts in a typical equity market) will be higher in absolute terms.

This is because they have a higher extrinsic value to lose due to the market's expectation of tail risk.