There is not a big difference between the two. Both are the same width, with the same general stateroom arrangement: the bed will be near the sliding glass doors to the balcony. The bathroom and the closets will be towards the door of the stateroom. It is the sitting/desk/general area that is the central part of the stateroom that will be a bit longer from end to end in the Cat D than in the Cat E.
I would say stay with the Cat E and spend the $150 on something else. Another consideration is that the Cat Es are in the center section of the ship with the bulk of the Cat Ds on the foreward and aft end. Look at deck plans in an old brochure if you can, or online to get an idea. In some places the Cat Es and Ds are interspersed side by side along the length of the ship.