The only way to answer your question honestly is to do the following (assuming you have two frames that are identical):
- String one with your regular Synthetic
- String the other with Natural Gut
- Bring both racquets to the baseline with you and, without looking at the stringbed, randomly grab one.
- Hit with that one for a few minutes, then grab the other (again try not to look at the stringbed).
After hitting for a few minutes, if you can tell the difference, determine which one you liked better, and you have your answer.
It also helps if you put brand new, identical overgrips on both. This way you won't know by the color or feel of the grip.