Base64 vs UTF-8

Often when dealing with binary data in a unicode context (e.g. JSON serialization) the data is first base64 encoded.  However, Python unicode objects can also use escape sequences.

What is the size relationship for high-entropy (e.g. compressed) binary data?

>>> every_byte = ''.join([chr(i) for i in range(256)])
>>> every_unichr = u''.join([(unichr(i) for i in range(256)])
>>> import base64
>>> len(every_unichr.encode('utf-8'))
384
>>> len(base64.b64encode(every_byte))
344

Surprisingly close!  Unicode has the advantage that many byte values are encoded 1:1; however, if it does have to encode it will be 2:1 as opposed to 3:4 of base64.  JSON serializing shifts the balance dramatically in favor of base64 however:

>>> import json
>>> len(json.dumps(every_unichr))
1045
>>> len(json.dumps(base64.b64encode(every_byte))
346

For the curious, here is what the encoded bytes looks like:

>>> every_unichr.encode('utf-8')
'\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~\x7f\xc2\x80\xc2\x81\xc2\x82\xc2\x83\xc2\x84\xc2\x85\xc2\x86\xc2\x87\xc2\x88\xc2\x89\xc2\x8a\xc2\x8b\xc2\x8c\xc2\x8d\xc2\x8e\xc2\x8f\xc2\x90\xc2\x91\xc2\x92\xc2\x93\xc2\x94\xc2\x95\xc2\x96\xc2\x97\xc2\x98\xc2\x99\xc2\x9a\xc2\x9b\xc2\x9c\xc2\x9d\xc2\x9e\xc2\x9f\xc2\xa0\xc2\xa1\xc2\xa2\xc2\xa3\xc2\xa4\xc2\xa5\xc2\xa6\xc2\xa7\xc2\xa8\xc2\xa9\xc2\xaa\xc2\xab\xc2\xac\xc2\xad\xc2\xae\xc2\xaf\xc2\xb0\xc2\xb1\xc2\xb2\xc2\xb3\xc2\xb4\xc2\xb5\xc2\xb6\xc2\xb7\xc2\xb8\xc2\xb9\xc2\xba\xc2\xbb\xc2\xbc\xc2\xbd\xc2\xbe\xc2\xbf\xc3\x80\xc3\x81\xc3\x82\xc3\x83\xc3\x84\xc3\x85\xc3\x86\xc3\x87\xc3\x88\xc3\x89\xc3\x8a\xc3\x8b\xc3\x8c\xc3\x8d\xc3\x8e\xc3\x8f\xc3\x90\xc3\x91\xc3\x92\xc3\x93\xc3\x94\xc3\x95\xc3\x96\xc3\x97\xc3\x98\xc3\x99\xc3\x9a\xc3\x9b\xc3\x9c\xc3\x9d\xc3\x9e\xc3\x9f\xc3\xa0\xc3\xa1\xc3\xa2\xc3\xa3\xc3\xa4\xc3\xa5\xc3\xa6\xc3\xa7\xc3\xa8\xc3\xa9\xc3\xaa\xc3\xab\xc3\xac\xc3\xad\xc3\xae\xc3\xaf\xc3\xb0\xc3\xb1\xc3\xb2\xc3\xb3\xc3\xb4\xc3\xb5\xc3\xb6\xc3\xb7\xc3\xb8\xc3\xb9\xc3\xba\xc3\xbb\xc3\xbc\xc3\xbd\xc3\xbe\xc3\xbf'