I asked around and was told that "ImageWithExif" is definitely not supported for Export with JPEG, so the example I gave above was misleading. On the other hand, I was informed that it should actually work as specified in the paragraph Jason noted:
'For the "ImageWithExif" element, the Exif tags are embedded using the MetaInformation option of the imported Image object under the name "Exif". The embedded Exif tags are automatically exported when exporting as JPEG.'
However, this currently isn't the case (in my 9.0.1 on Windows):
test =
Import["http://www.exif.org/samples/canon-ixus.jpg",
"ImageWithExif"];
test // Head
(* Out: Image *)
"Exif" /. (MetaInformation /.
Options[test, MetaInformation]) // Length
(* Out: 41 *)
retest =
ImportString[ExportString[test, "JPEG"], "ImageWithExif"];
retest // Head
(* Out: Image *)
"Exif" /. (MetaInformation /.
Options[retest, MetaInformation]) // Length
(* Out: 0 *)
I've passed this along to our team.