If you get the Mountune or the ST200 box you will draw air from 2 locations. One is the stock location, the plenum above the radiator which is good for keeping things quite but obviously compromised because it is heated by having the radiator right below it. The 2nd location is down by the fog light which is clearly better. Both locations will combine in the airbox for a slightly warmer than ambient temperature air mix heading to the turbo. This clearly better than stock USDM. The turbo will be sucking this air in just like sucking a milkshake through a straw.
If you keep the stock USDM airbox and add a Big Mouth, the air is coming from in front of the radiator and is not heated by it, thus giving you a cooler charge of air. When you are moving, that cooler air will also lightly pressurize the airbox and the tube all the way to the turbo inlet. Instead of the turbo sucking to get air, the air will be trying to get into turbo on it's own. This may or may not help make any power but what it does do, is spool the turbo sooner thus increasing throttle response. Imagine the milkshake is now being pushed through the straw. That is less work for the person/turbo doing the sucking.
Now if you add the Big Mouth to the ST200/Mountune intake you have 2 locations receiving ambient air. The restriction is less and the air is cooler than in example 1 but you do not get the positive pressure advantage from example 2.
Taking all this into consideration my choice is Big Mouth with stock airbox. I do feel like the throttle response improved and the car feels peppier getting on on-ramps or just passing someone on the freeway.
As an alternative, one could take a ST200/Mountune/DIY add a hose down to your fog light location and install it so outside air would forced into the tube. Then block the stock inlet location inside the airbox (even with duct tape) and it would provide a similar pressurized effect as the Big Mouth with stock airbox. This would be very cheap for you budget minded folks but I think the Big Mouth is a shorter path with less pressure loss.
FYI, I don't work for Velossa Tech, Mountune or any other car related organization. This just my opinion.