Base64 encoding of strings I have read everywhere that base64 encoding of unique binary/hex values results in unique output.  The following two string encode to virtually the same output.

{"alg":"SHA1","typ":"JWT","iat": "Sep  8 2018  8:51AM", "exp": "Sep  8 2018  9:11AM"}


gives output:

eyJhbGciOiJTSEExIiwidHlwIjoiSldUIiwiaWF0IjogIlNlcCAgOCAyMDE4ICA4OjUxQU0iLCAiZXhwIjogIlNlcCAgOCAyMDE4ICA5OjExQU0ifQ==


while

{"alg":"SHA1","typ":"JWT","iat": "Sep  8 2018  9:10AM", "exp": "Sep  8 2018  9:30AM"}


gives output:

eyJhbGciOiJTSEExIiwidHlwIjoiSldUIiwiaWF0IjogIlNlcCAgOCAyMDE4ICA5OjEwQU0iLCAiZXhwIjogIlNlcCAgOCAyMDE4ICA5OjMwQU0ifQ==


The only the difference between the two is: ExQU0ifQ== and MwQU0ifQ== at the end of the output.

Only the times are different in the two strings; is that why the difference is so minute?
The whole purpose of base64 encoding is to take arbitary byte values and transform them into a limited subset of ASCII characters so that they can be "safely" sent (older transmission protocols could garble some byte values because e.g. some raw bytes had special meanings to those protocols; the only data that would be expected to not be changed was plain ASCII text.)

It does this by encoding three bytes (24 bits) into 4 characters (each of which has 64 values, so encodes 6 bits as $2^6 =64$) in a pretty simple fashion (some extra rules for incomplete groups). So every aligned identical three bytes in two messages get encoded into the same 4 characters every time. So changing 1 byte only will change at most 2 adjacent characters in the result, if you study the transformation this is obvious. 

There is no expectation of more changes: it's just another representation of the same bits in the same order, and easily reversed on the receiving end.

In fact (IMO) in any sensible protocol your JSON-formatted data should be sent as is, as it's already all ASCII, and base64 encoding adds nothing but using more bandwidth. When encrypted it should be random-like binary data and could be sent in base64 format (and this is in fact customary: PEM and PGP send their messages base64 encoded, and very often binary mail-attachments as well.)