There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local Volatility and not producing a Delta "true up" using Stochastic Volatility that is common among other banks. In other words, Delta of the autocallable notes is higher in magnitude under Local Volatility compared to Stochastic Volatility. Since the bank thought it was holding more (negative) Delta as a result of the Local Volatility model, they bought too much stock to hedge and had large losses when the market declined.
Can someone provide an intuitive explanation of why Delta is higher in autocallable products under Local Volatility compared to Stochastic Volatility? The price of the product is different under the two volatility models on account of vol-of-vol differences, but it's not entirely clear to me why the Delta difference is in this direction.