Drupal - Conditionally display one of two fields in Display Suite?

Use the field formatter conditions module: https://www.drupal.org/project/ffc

This will give you the same options that you have on a blocks (and more). So you can show the field based on any url pattern just as you would blocks:

http://cl.ly/image/2A2Y373Y3e1J

Hope this help.

Your only option is a custom code field. There have been attempts to make conditional fields possible through the UI, but it was too complex.