Nashorn isn't actually used in Java's WebView (which my project leverages). Nashorn is used elsewhere in the JRE and replaces Rhino from prior releases, but WebView has used something else entirely: JavaScriptCore. Details:
http://stackoverflow.com/questions/30104124/what-javascript-...But essentially on performance, it's comparable to a desktop browser but still slower than I'd like. Java 9 should support HTTP 2 and async HTTP by default, which might help. And I've been looking into short-cutting some of the in-memory rendering but haven't had any breakthroughs yet.
As far as JavaScriptCore engine specifically, it's the default in WebKit so there should be good performance data out there on it.