Is there any advantage in wrapping a BufferedOutputStream around a ByteArrayOutputStream instead of just using the ByteArrrayOutputStream by itself?
Generally BufferedOutputStream wrapper is mostly used to avoid frequent disk or network writes. It can be much more expensive to separately write a lot of small pieces than make several rather large operations. The ByteArrayOutputStream operates in memory, so I think the wrapping is pointless.
If you want to know the exact answer, try to create a simple performance-measuring application.
Absolutely none. Though BufferedWriter and BufferedReader do offer extra functionality were you to be operating on strings.
ByteArrayOutputStream is not recommended if you want to get high performance, but one interesting feature is to send a message with unknown length. For a better comprehension about how these two methods work, see http://java-performance.info/java-io-bytearrayoutputstream/.