How would I express XML tag attributes in JSON?

This approach supports inverse transformation to XML:

{
    "folders": {
        "folder":{ 
        "@": {
            "id": "123",
            "private": "0",
            "archived": "0",
            "order": "1"
            },
        "#": "Shopping"
        }
    }
}

It works correctly with js2xmlparser.

Perhaps:

{
  "folders": [
    { "id":123, "private":0, "archived":0, "order":1, "title":"Shopping" },
    ...
  ]
}

Because there is not an exact correspondence between XML and JSON, you are free (e.g. have to define) how the two data-structures map. For instance, in the above, the "folder" element is implicit in the nested objects in the "folders" array.

This could be expanded as in:

"folders": [{"folder": { .... }]

Etc, but there is still the problem of not being able to capture content+attributes as consistently as XML. In any case, your data-structure -> JSON|XML serializer likely works in a particular way (and please, please, use a library, not "hand-rolled" JSON-string-munging). That is; the format of the XML and JSON should be uniformly dictated (somehow) by the data-structure for transmission.