I've mentioned this before, but just to repeat - there is a known performance issue with Awesomium, and I'm trying to get them to fix it. However the Awesomium team have a lot of other priorities so I'm not sure when they'll get round to it.
If the performance issue is resolved, Awesomium should *always* be faster than the Chrome browser. However due to the performance problem some machines (usually lower-end or older computers) end up slower than the Chrome browser. Again, we know why this is and what needs to be done, so hopefully it can be fixed soon.