Bandwidth bottleneck on Pro... same thing happened between the PS4/XB1, but to a lesser extent (obviously). In this specific game, you had 1080p vs 900p + much better performances on PS4 which is greater than the GPU difference.
Another interesting example regarding PS4 -> X1 would appear to be Wolfenstien 2. We know that iD battled to get performance up on X1, apparently because the game's many buffers simply didn't work well with the small amount of esram. So in the case of both X1 and PS4 Pro, I think we're seeing times when the available bandwidth (from DDR3 in the case of X1 and main memory for PS4Pro) makes the system fall below the performance you might otherwise expect.
This isn't to say PS4Pro is a bad design of course, Sony wanted to maximise bang for buck and likely wouldn't have known (or cared) about X1X. Extra bandwidth would probably have added significantly to BOM in a way that the relatively modest increases in die area and GDDR5 speed bins didn't.
I do think MS deserve credit for the X1X too. The say they did a huge amount of profiling of games on X1 and ran a lot of simulations on removing bottlenecks. The huge 12 channel memory controller (in comparison to the PS4Pros 4 channel) would seem to indicate that they were keen to minimise latency and the impact of contention, and maximise the real world throughput of the SoC. That could be an area where an extra year of R&D showed results.