How are you supposed to prove a negative, "No son, we don't love your sister more." I would say that you two should call a family meeting, set the ground rules that everyone will get a chance to talk uninterrupted for a specified time, all comments and sentences will begin with "I", no "You always..." statements are allowed. The goal of the family meeting will be to discover how they can feel cared about in a way they need- remove the loving the other one more construct- that's tired, old and unproductive. What does each one of them need individually to feel they are cherished, appreciated, supported, etc.? Then you have to decide whether their requests of you are legitimate and whether or not you can give them what they need. Don't be bullied or emotionally blackmailed and triangulated by both of them in their attempts to one up the other. This will be an honest and courageous step in ending this long-running complaint. Good luck!
Q
I have a 19-year-old son and an 18-year-old daughter. Each thinks we love the other one more.
A
This sibling rivalry and jealousy probably has a considerable history in your family. One of the brothers in the Smothers Brothers comedy team used to always whine, "Mom always loved you best." If your two, at these ages, are still making you two feel guilty about loving the other one more, all of you have been dancing habitually to a rhythm no one seems able to or wanting to stop.