Most DIY-ers will have experienced the frustration of self-inflicted screw damage due to the use of the wrong screwdriver type (or size, but let's keep that factor out of this particular question).
My research thus far indicates that the key difference between Phillips and Pozidriv screwdrivers is the fact that Phillips drivers are designed to "torque out" of the screw head if over-torqued, which increases the likelihood of material damage and distortion to both screw head and driver. Pozidriv, on the other hand, is designed such that it cannot jump out if over-torqued.
The same source mentions the both screwdriver and head should be of the same type:
Phillips drivers should not be used with Posidriv screws (and vice versa) as they tend to ride out of the recess and round the corners of both the tool and screw recess.
While I can understand this for the Phillips screwdriver on a Pozidriv head, I struggle to see why this would be an issue for the reverse combination, since the risk of torque-out is absent and the screw head groove geometry appears to be quite similar.
Here is a side-by-side comparison of the two driver types (Phillips left, Pozidriv right):