According to GameSpot http://www.gamespot.com/articles/ps4-pro-has-replaceable-hard-drive/1100-6444663/ it looks like the PS4 Pro will come equipped with a SATA III interface! This means a max 6 Gbps speeds rather than the antiquated SATA II's 3 Gbps.
What this means is faster load times, especially if you're using a Solid State Drive. Theoretically, this will help alleviate the Drive transform issue where you activate it, and Sora stands there for several seconds before the transformation is complete. Even if you aren't swapping the included HDD for an SSD, this and other memory-based time wasters (like activating BBS's D-Links) should be at least somewhat alleviated compared to the PS3 version, due to the entire game being read from the HDD (or SSD) rather than pieces being transferred from disc to RAM when needed, which is why these load times are so monstrous.
TL;DR: Load times will be marginally improved on PS4 and Pro due to game installed to storage. Load times WAY improved on Pro if installing an SSD because 2x read speed thanks to SATA III.
What this means is faster load times, especially if you're using a Solid State Drive. Theoretically, this will help alleviate the Drive transform issue where you activate it, and Sora stands there for several seconds before the transformation is complete. Even if you aren't swapping the included HDD for an SSD, this and other memory-based time wasters (like activating BBS's D-Links) should be at least somewhat alleviated compared to the PS3 version, due to the entire game being read from the HDD (or SSD) rather than pieces being transferred from disc to RAM when needed, which is why these load times are so monstrous.
TL;DR: Load times will be marginally improved on PS4 and Pro due to game installed to storage. Load times WAY improved on Pro if installing an SSD because 2x read speed thanks to SATA III.