Going from Breadboard to PERMANENT circuit but have Arduino shields attached?
A breakout board is for testing the functionality of a part, without having to first read it's electrical properties, deliver power to it, solder pins to it, etc.  It decreases the confounding variables when adding it to your existing system; in other words, it should act as a plug-and-play black box.  Once your system functions with all it's disparate parts, then you try to figure out how to move the part from the breakout board onto your own board. (including the capacitors, resistors, etc that it needs.)

A breakout board shouldn't be used if you are going to production, because it's too expensive.  Usually the chip is about $1, but the board is about $20.  You're paying Arduino or whomever for the work they did in figuring out how to put the board together.