Digital prices under matched normal and lognormal models

A normal model and a lognormal model are each calibrated so that they give the same price for a vanilla call at a particular strike. Which model gives the higher price for a digital call at that strike, and why?

The normal model gives the higher digital price. A digital is $-\partial C/\partial K$. Viewed through Black-Scholes, a normal model corresponds to implied vols that fall as strike rises. Differentiating $C=C_{BS}(K,\sigma(K))$ gives digital $=$ lognormal digital $-$ vega $\times\sigma'(K)$, and with $\sigma'(K)<0$ the extra term adds value.