This question is regarding the order of precedence for the media-types of the HTTP Header \"Accept-Encoding\" when all are of equal weight and has been prom
I believe somewhere in the RFC, or in a related RFC, it states that the first is preferred for all fields of this format.
However, in the special case of gzip vs deflate, you should probably use deflate if you can due to lower overhead (fewer headers and footers, and although it still has an adler32 checksum, it doesn't have a crc32 on top). Other than that they are exactly the same. The actual data is compressed in the same way for both. This means deflate is both faster and produces a smaller output. Both of these become far more important on a page under heavy load. Most of the extra headers in gzip are things like unix style file permissions, which are useless in this context anyway.
Really, clients should want to be served gzip due to reliability and servers should want to serve deflate due to performance. The extra overhead is much more important when it happens thousands of times a second than when it happens once for every page you load.
On my own sites I check for deflate first and use that if I can, then I check for gzip. If I can't use either, I just send in plain text. I don't know what language you are using but it's about 5 lines of ASP.NET to do that.
There is no client side preference here. Just pick one what you (the server side) would prefer.