There are a few reasons why one receives more cash value for trading their diamond versus selling it for cash. The first of which is that a diamond retailer intends to make a profit off of the diamond you are trying to sell to them. If you are attempting to sell to a third party your diamond will have depreciated in value simply because it is not under the glass in a jewelry store. The way to get the most out of your diamond is to trade it toward the purchase of a newer one. This is because if you are trading your diamond toward a more expensive one the jeweler is making the money he needs, and therefore can offer you a greater sum for your diamond.
This seems to be a universal constant in the world of second hand items. You will always be paid more for your item if you are willing to trade for store credit. As a corollary this method of trading your diamond is only practical if it is a bigger or better diamond that you are seeking. If you want to trade the value of your diamond for other goods and services you must seek an alternate root that will result in obtaining a lower amount of value for your diamond. By trading in your diamond you are reinvesting in the jeweler and the market it was purchased from, because of this you will always receive a greater value by trading in your diamond.