The image processor in the P3Pro is the Ambarella A9, a 2.5 year old 1st Generation 4K/UHD chip (Much deeper information here:
http://forum.dji.com/forum.php?mod=redirect&goto=findpost&ptid=19599&pid=144431&fromuid=6139
First up video - All 4K/UHD video is recorded at 60Mbps, which is roughly 7.5MB/s. Any "Class 10" card is, by definition, capable of recording sequential data at 10MB/s. Spending more is your choice, but it will only help you when extracting data to your computer.
Still photography, particularly rapid fire or multiple exposure (AEB) generates much greater data, up to 200MB/s, but there appears to be a bottleneck in the firmware that restricts the SD card interface bus to "Normal Speed", 12.5MB/s (SD bus specification 1.0). The chip, at a minimum must support High Speed, 25MB/s (SDXC, SD specification 2.0), put potentially supports UHS-I SDR104 (104MB/s bus) and I have an inquiry into Ambarella to find out what the maximum bus speed they support.
SD Bus speeds can be controlled by firmware, and DJI may have chosen to restrict the SD bus to "Normal Speed" because they (mistakenly, IMHO) believe it will improve compatibility with older/slower cards. Alternatively, DJI may have chosen to throttle the SD bus because it doesn't matter for video, 12.5MB/s is plenty fast enough for video and photography is a secondary concern.
[Side,side note - I will be happy to field test beta firmware that enables faster transfer speeds, DJI]