Can anyone recommend whether I should do something like:
os = new GzipOutputStream(new BufferedOutputStream(...));
or
os = new BufferedOutputStream(new GzipOutputStream(...));
Which is more efficient? Should I use BufferedOutputStream at all?
I suggest you try a simple benchmark to time how long it take to compress a large file and see if it makes much difference. GzipOutputStream does have buffering but it is a smaller buffer. I would do the first with a 64K buffer, but you might find that doing both is better.
The buffering helps when the ultimate destination of the data is best read/written in larger chunks than your code would otherwise push it. So you generally want the buffering to be as close to the place-that-wants-larger-chunks. In your examples, that's the elided "...", so wrap the BufferedOutputStream with the GzipOutputStream. And, tune the BufferedOutputStream buffer size to match what testing shows works best with the destination.
I doubt the BufferedOutputStream on the outside would help much, if at all, over no explicit buffering. Why not? The GzipOutputStream will do its write()s to "..." in the same-sized chunks whether the outside buffering is present or not. So there's no optimizing for "..." possible; you're stuck with what sizes GzipOutputStream write()s.
Note also that you're using memory more efficiently by buffering the compressed data rather than the uncompressed data. If your data often acheives 6X compression, the 'inside' buffer is equivalent to an 'outside' buffer 6X as big.
Read the javadoc, and you will discover that BIS is used to buffer bytes read from some original source. Once you get the raw bytes you want to compress them so you wrap BIS with a GIS. It makes no sense to buffer the output from a GZIP, because one needs to think what about buffering GZIP, who is going to do that ?
new GzipInputStream( new BufferedInputStream ( new FileInputXXX