In chrome, I'm getting extremely similar times for the two approaches without caching (I am in-network, so my roundtrips are ~1ms). With the style.css fully cached, I'm getting ~15ms faster on the sideband approach than with inline styles.
Can you expose your methodology, or are you using a common tool for testing these things?
It looks like inline performs better on firefox and not on chrome - I just made a bunch of attempts both ways, and I'm seeing cached sideband as significantly better on Chrome, and only roughly equal on firefox.
I was not expecting to see such a difference between the two browsers, but I'm not familiar enough with firefox to guess what's causing it :-\
Can you expose your methodology, or are you using a common tool for testing these things?