2 Different Types of Brolly Boxes?

I see there are 2 different types of Brolly Boxes. One is a shoot though and they other is a bounce. I usually use shoot through umbrellas so would a shoot through Brolly Box be much different?

The amount of difference depends on the design of the brolly box. The whole point of moving from one modifier to another is to achieve a different effect, or to better control the spill of light. A shoot through umbrella literally throws light everywhere - there's a lot of wasted power since the light is not focused in only one area, but is left to fall wherever physics allows it.

A shoot through brolly-box, depending on how it is constructed, should be more efficient than what you are using now. The reflective/bounce umbrellas are also efficient, but I'll leave the numbers to someone more versed than I.

Both designs will control spill signifcantly better than your shoot-through. That said, if the design has a lip of black material, it will control it even more so the light isn't bouncing unrestrained off nearby walls - think of it like barn doors for a softbox. Then there's grids which help even further.

What are you firing into it?