Basically you only have three input fields - where the user only needs two.
First, I would add some short help - an explanatory text in a modal, a hover icon (see other questions and answers for that) - to explain what the difference in terms of cost is, but leave out the difference regarding the needed codes. I would make sure to keep it short, but complete. Get to the point in the shortest sentences, but don't avoid depth.
Interaction with the form
Second, the form already can decide what the user needs: If he checks local, you can easily just disable the ABA Code field, hinting the user what information is needed. If he switches back to priority, you can again make it available.
When the user then clicks into the ABA Code field and start typing, you can just disable the Swift Code field. Enabling it again could happen by deleting the text in the already filled field.
Learning from mobile
On mobile devices it's still hard to type (on a touch screen without physical feedback). So on mobile devices you always will find great hints on how to simplify a users life when it comes to "type less".
If you want to be nice, add a (x) delete icon inside on the right hand side in the field, so the user can easily just dismiss his edit. This is a common pattern from mobile devices (for e.g. Google Maps) to avoid unnecessary typing (or holding the delete button on a touch screen).
Another thing that you can learn from Google Maps is the "switch button". When you want to enter a route, Google doesn't care if you have correctly entered the start and target points. You can just hit a "two arrows" button on the right hand side between them and the values get switched. You could offer the same interaction as well: When the user enters the Swift Code and he clicks the button, you switch the text to the ABA Code field and disable Swift. Make sure to blink (or hint in another way) the "priorty" checkbox so the user knows what happened.
There have already been redesigns of payment gateways that work with known real world interfaces, namely the card itself, to help the user to quickly find the needed information.