They are pretty much interchangeable, and people will always know what you mean whichever word you choose. However, there are a few subtle difference, because „zugeben“ usually means that you admit something you were confronted with, while „gestehen“ means you confess something, which can be out of the blue.
And you are right, in your example „Du mussmusst gestehen oder zugeben, dass sie sehr nette Person ist.„ you can use „zugeben“ to indicate that you are looking for agreement. This is another subtle difference: „du musst zugeben“ often means „you have to agree/admit, that...“ while „ich muss gestehen“ often is an admission of guilt. If you are explaining to your mother why you failed a test, you could say „du musst zugeben, der Test war schwierig“ oder „ich muss gestehen/zugeben, ich habe zu wenig gelernt.“
A notable exception is when you confess someone your feelings, „ich muss dir etwas gestehen“ or „ich habe ihm meine Gefühle gestanden“ are common phrases, while „zugeben“ doesn’t work (unless, as I mentioned in the beginning, someone accused you of your feelings and you maybe even denied it, but now admit it - then zugeben would be fine.)
