A friend has the same problem pairing the JBL Charge to the Note 3 though the JBL Charge pairs to everything else without a hitch.
I can't get the Note 3 to pair to my Bluetooth TV sound bar even though it pairs with the Note 8, S3 and S4.
Furthermore, these are the only two devices that the Note 3 will not pair with of the half dozen devices I have.
UPDATE: Trying to pair a couple of more times with the JBL Charge and the Note 3 resulted in a successful pairing. The issue I was having was actually getting into "pairing mode" on the JBL Charge.
UPDATE DEUX: Digging out the instruction manual for my VIZIO sound bar I found that I was not really getting the sound bar into pairing mode, confused on the particular light show on the sound bar I was supposed to see. Once I got that straigthened out the Note 3 paired in a flash. Can't blame the phone for operator error.