Last I checked, compression wasn't supported by all browsers all the time. It needs to be done dynamically depending on the settings the browser allows.
nginx or varnish can do that (with more or less correct rules).
In practise, I usually disable compression everywhere and let the CDN handles it.
The CDN is configured to compress on the fly and I am very confident that CloudFlare/Akamai are doing that much better than a broken snippet of nginx settings from stack overflow.
As one would expect, S3 can certainly support various browsers. It ends up being just like content negotiation, in that you have multiple representations that could be served from a particular resource, depending on what headers are sent.
I'm not sure if it's still like that, since I'm not using S3 for that right now.
I'm not an expert by any means, but I think you can manually gzip your content and add rewrite rules to Apache (don't know about other servers) to use the .gz versions. I think this is the only way for compressed content to be cached by Apache, but I'd love to learn if I'm wrong here.
nginx or varnish can do that (with more or less correct rules).
In practise, I usually disable compression everywhere and let the CDN handles it.
The CDN is configured to compress on the fly and I am very confident that CloudFlare/Akamai are doing that much better than a broken snippet of nginx settings from stack overflow.