Well remember, WebAssembly just a different representation format for the same instruction set, executed by the underlying virtual machine (v8, spidermonkey, etc). So you should expect to see much of a performance difference.
The main benefit of WebAssembly is so that we can write code using our favorite languages (not just javascript!) and compile to a common binary format the browser understands. The objectives of WebAssembly never had anything to do with performance.
> The main benefit of WebAssembly is so that we can write code using our favorite languages
JavaScript is already common format that browser understands and there are implementations for a lot of languages translating them to JavaScript. So WebAssembly definitely is about performance, because using other languages is already solved problem.
As far as I understand you can call JS APIs from WebAssembly, which means you use the already available DOM APIs. I don't know exactly what the calling convention from WASM to JS looks like, but I guess it's specified somewhere.
The main benefit of WebAssembly is so that we can write code using our favorite languages (not just javascript!) and compile to a common binary format the browser understands. The objectives of WebAssembly never had anything to do with performance.