Okay im a little confused as to your question so here goes my answer (former Gate Agent / Flight Attendant)....
Say you spend $300 on a fare New York - Orlando. You want to change to say the next day. Each airline has their own "fees" associated with changing so for sake of conversation United's is $100. Next you must pay any difference in the fare. If its less, you get a refund of the difference minus the $100 change fee. So....
Example 1, more expensive flight
First Flight was $300
New flight costs $375
To change to this flight will be $175 extra (Change Fee + Difference in fare)
Example 2, Cheaper fare
First Flight was $600
New flight is $300
You will get $200 back from the airline (Difference in fare - $100 change fee)
That answer your question? Ive done both and only once has it been cheaper.
Clint
Gosh,you're a great person to ask then!

Here is the rundown (confused by what actually happened after I hit "change").
It was to change tickets to a different airport in a different state (long story). So when I was on the website to change, it said it would be $48 for the way there and $20 for the way back, plus $150 change fee. Totally fine. So I go ahead and proceed, give them the credit card to charge the amount to, but it shows now that its just $170 total to change (even better, cheaper than I thought). When I read the confirmation email, it said that they will charge my credit card $20 per ticket (its just me going), and then the $150 for the fee. Again, totally fine...just confused why it originally said it would be $48 for the first leg and another $20 for the way home.
So, anyway, basically, I am just really confused what will happen with the bank accounts. The original $543 for the first ticket came out of the checking account, and the $170 went on the Disney Visa. Wondering if they refund the original amount and then re-charge it?
Also, maybe you will know this crazy thing to- when I was changing the flights, it had me pick new seat assignments (there was one seat left). When I print out the confirmation, it still had my original seat assignment for the portion of the flight that stayed the same, not the new seat that I had just chosen (which was perfect because I am meeting my mom in Denver and had originally picked seats next to eachother). No big deal either way there...just trying to understand and learn more about how things like this work!