I'm not familiar with either project but a big one is that Awesomium has a C# and .NET API. That alone could be reason for some to choose it.
Our .NET wrapper is open-source and up on GitHub: https://github.com/khrona/AwesomiumSharp
Btw, AwesomiumSharp has recently been re-written and now includes a drop-in WebControl component for WPF that you can hook up to your application with XAML. We're about to stage a major re-launch of the wrapper + new 1.6.2 SDK release in a couple days.