I have an Apache HTTP server which is configured with mod_deflate to compress content "on the fly".
Is there any benefit if I serve a compressed sitemap.xml.gz file, or should I rely on mod_deflate to compress resources?
GZIP offers superior compression in most instances, but XML sitemaps just aren't that large to begin with. I would say that you shouldn't worry about it.
Unless you have some very sizable sitemaps (ie: Approaching the 50,000 URL limit), I would say that the server's compression should be sufficient - at least to avoid the hassle of manually compressing them yourself.