Besides the obvious (one is a type, the other a class)? What should be preferred? Any notable difference in use cases, perhaps?
In terms of python 2.7 and 3:
io.BytesIO is an in-memory file-like object that doesn't do any alteration to newlines, and is similar to open(filename, "wb"). It deal with bytes() strings, which in py2.7 is an alias for str.
io.StringIO is an in-memory file-like object that does do alterations to newlines, and is similar to open(filename, "w"). It deal with unicode() strings, which in py3.x is an alias for str.
py2.7's old StringIO.StringIO is an in-memory file-like object that does not do alterations to newlines, and is similar to open(filename, "w"). It deals with both unicode() and bytes() in the same way that most obsolete python 2 string methods do: by allowing you to mix them without error, but only as long as you're lucky.
Thus py2.7's old StringIO.StringIO class is actually more similar to io.BytesIO than io.StringIO, as it is operating in terms of bytes()/str() and doesn't do newline conversions.

What should be preferred?

Don't use StringIO.StringIO, instead use io.BytesIO or io.StringIO, depending on the use-case. This is forward compatible with python 3 and commits to bytes or unicode, rather than "both, maybe".
What is the difference between StringIO and io.StringIO in Python2.7?