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Well, it depends on what you what to do, definitely.
Edison + Arduino Expansion Board: Allow you to use a more extended way to interact with physical ports, (Digital pins, Analog Pins, USB, SDcard ...)
Edison + Breakout Board: This one allows you to work with the Arduino IDE or the terminal console but without the physical ports included in the Arduno Expansion Board. If you don't need those you can use this.
This is a document about some Shield Tests Report with results and modifications to make it work.
In the Software & Documentation Section you will find more information related to the boards.
I hope you find this helpful.
Thank you for the quick reply CMata and also providing me with the information to make an informed buying decision.