Mini ITX PSU and Power Brick Wattages
It's like the weakest point in the system.

For example on a car the tires may only be good up to 130 mph but the engine can go up to 140 mph. Or something like that, I'm not a car person.

Really it's being a bit cheap to only stock the 102W supply. If you want a decent 12V supply you should look at an ATX power supply. In fact the pico PSU could be replaced by one of these entirely. Only go for that brick if size is a problem. Even then, you can find a 150W ATX PSU in a small form factor nowadays anyway.

Additionally I would find it very difficult to believe that the pico PSU can provide 150W without cooking itself. Looking at it, the inductors are small surface mount types, probably not greater than 4-5 amps continuous. And I can't see a power transistor; if there is one, it would need some serious heatsinking. (Think about your computer power supply: 300-400W, about 2x as much as the pico PSU but with a large heatsink, plus it has a fan. Yes, one operates off 12V and one off mains, but the mains PSU's FET will actually have less current flowing through it and probably run cooler.) I would like to be wrong, but I can't see it.