3 of them do give you the differences back, and they are not the big 3.
Southwest, Alaska, and JetBlue have the most favorable policies for the consumers. If the fare drops after you buy the ticket, these 3 carriers will give you the differences back.
The big 3? Delta, United, and American? No.
With the big 3, this is what you can do. The change fee is $200. If the fare drops more than $200, you can change the ticket, pay the $200 change fee, and then you can receive the credit for whatever is left.