Oh, it's as simple as it sounds. The placed the motherboard so the SOC is facing down. Amazing.
No, it's complicated. I dismantled my PS4 completely about 5 times now, and voided the warranty as soon as I got it in november (which I do with everything, really). I'm still not 100% sure about a lot of details, but here it goes...
The centering of the ODD, the HDD being on top, and the almost complete lack of cables, all require an inverted motherboard. Otherwise it would have added an inch in height. It allows a lot of space saving without ever impacting the cooling efficiency, there isn't a milimeter wasted. The HDD is right on the motherboard plane, so no cables, and still easily accessible. Heat rises, and the top plate happens to be the motherboard shielding which is very well cooled, so there's no heat accumulation under an isolating plastic. If placed vertically, any heat source will hugs the shielding plate anyway, but it's less efficient, it's probably a little noisier vertically? I don't know.
The fan turns toward the wall, and it allows a clever trick of increasing pressure when combined with the split fins density. Few people realize that fin surface area is similar between the XB1 and the PS4, so cooling capacity with the same flow is also similar. The holy grail of heat management is about pressure, not free air flow. Because pressure allows thin laminar flow, deeper fins, and higher fin density, with lots of surface without wind noise associated with flow. That makes a system incredibly smaller for the same cooling efficiency. Trying to get a lot of pressure without needing a very high RPM is an art in itself, but that's exactly what the heavily slanted fan blades are doing in a centrifugal design. Prioritize pressure.
The Power supply is at the end of the air path, and it can tolerate the higher air temperature compared to the HDD or ODD, so it's basically cooled for free since there's plenty of pressure available and the PS components are widely spaced. Being at the end of the path, it doesn't impact the other components temperature.
The split intake above and below the fan is reducing air speed by half, reducing turbulence by half. This split also creates a very wide laminar flow on the top and bottom of the case (isolates the PS4 from stacked components), and also a thin layer of cold air between the shielding and the motherboard on both sides. This isolates the hot SoC cooling from the rest of the system, each path is independent and isolated from each other by a layer of cold air. The holes and embossing of the shield plates are precisely designed to balance the pressure available to keep everyone on the motherboard happy.
XB1 is using an opposite design, low pressure, like a PC. Therefore they cannot have a thick heatsink and have to spread it very wide (thicker would bog down the fan and stop the flow, requiring higher RPM). They have 3 inches high available and still can't have thick heat sink. The rest of the case is a big waste of space, and the motherboard itself has a negligible air flow, much less than the PS4. Maybe they could fit a power supply there, but it's possible that the fan design prevents them from having enough pressure to cool it, and It would be in the wrong path (the intake) while a PS should always be at the end of a cooling path. The reason is about operating temperature. Sensitive stuff goes before the SoC, and non-sensitive stuff after.
I'm troubled by the fact that some people were brainwashed into thinking that it's as simple as
"it's bigger, so it can be less noisy". Or even that an external PS with it's own fan makes a positive difference by itself. It's a good exercise to look back at the "prediction" thread where people thought the PS4 would be very noisy, or much bigger than XB1, or would have an external PS. Rules of thumbs break down when it's not just a guy building his own PC. Airflow and cooling is an insanely difficult topic when you stop using rules of thumb and want to maximize everything. I won't pretend I understand it all, but I understood enough to be right about it, long before we had the consoles in our hands.
"This device would have been better with an external PS with it's own small fan"
-- said no one ever in the history of consumer electronics. The question should be about what compromises or additional development were necessary to avoid having an external power supply with a fan.