Generally with the legacy airline, you won't get any credit at all.
When you get a flight for a lower fare, essentially what happens is your current flight is canceled, your fee is refunded, then the flight is rebooked at the lower fare using these refunded proceeds. Given this, the legacy airlines charge a cancellation or rebooking fee to do this for any occasion, including a refund for the lower fare.
Delta's appear to have gone up to $200 (from $150).
Based on the fare rules, you may have to pay a service fee and/or a difference in fare. For travel within the 50 United States, Canada, Puerto Rico and the U.S. Virgin Islands, the fee is $200 for Delta-marketed flights.
Thus, the first $200 of the refund is eaten by the change fee, and the difference in fare, per ticket, would need to exceed this to get anything back.
That said, the (relatively) new passenger bill of rights put out by the FAA entitles someone who purchases a ticket the option to cancel for a refund within 24 hours.
If you are within this 24 hour window,
you can take advantage of the price difference. Otherwise, I doubt the fare difference is enough to exceed the change fee.
Hope this helps, and sorry for the answer!