Phillips isn't properly designed for power or hand tools. If it strips with a screwdriver, it's definitely going to strip with a drill. I've rarely seen power-driven Phillips screws that didn't have some sign of stripping, even using torque limiters and even on things fresh from the factory.

At least flat head takes uneven torque from hand tools well. It also allows improvised tools to be used in the field. If I'm working on say an off-road vehicle like a dirt bike, I'm going to tend to use just one size of hex bolt (usually 10mm) and flat heads for the screws.