Just got them (Everdock Duo) for my wife and I. Love it. I am docking a iPhone 6 with a Neo Hybrid case. I used the thin insert, but cut the bottom off, so that it is just the back. The case required it, but works perfectly. Given cases are different, YMMV. My wife has a different case, not as thick on the bottom, and we didn't have to modify her insert. I use the thin insert for the second slot for my iPad 2. Wife uses the thick one for her iPad mini.
Word of caution for Lightning cables... the inserts provided fit the stock cables and may not fit 3rd party cables, but will fit Apple cables. I have a 3rd party cable that I got because I wanted black... didn't fit. Same with the 30 pin connectors... the dock is set up to use the Apple cables.