I have used WebView quite a bit and usually the performance was perfectly fine and very usable.
- Html5 compliance is good.
- JavaScript performance varies but I found it about one third the speed of a recent version of Chrome according to Google's V8 benchmark (which Chrome is presumably tuned against).
- Rendering performance didn't seem to be much of an issue.
- Very intensive HTML Webapps such as some in the Chrome experiment library did not start up as quick as in some other browsers.
- WebGL is not supported so sites which fall back to software rendering of graphics from WebGL are much slower.
The biggest issue I had with WebView is that it is not quite as stable for cutting edge features and intensive use as other browsers, but not really any serious performance issues.
Here are a few benchmark stats (WebView version used was sourced from JavaFX 2.2 build 9):
Compliance
Running a html5 test to test html5 compliance (scores out of 500):
Chrome 19 402 + 13 bonus points
Firefox 12 345 + 9 bonus points
WebView 2.2b9 296 + 7 bonus points
IE 9.0.6 138 + 5 bonus points
Running an acid3 test, webview scores 100/100 same as the other test browsers, but, like IE9, the final rendering has a slight imperfection.
Javascript
Sunspider Javascript benchmark (lower is better):
IE 9.0.6 146.7ms
Chrome 19 151.5ms
Firefox 12 185.8ms
WebView 2.2b9 199.5ms
Google V8 Javascript benchmark (higher is better):
Chrome 19 15323
Firefox 12 9557
WebView 2.2b9 5145
IE 9.0.6 3661
Mozilla Kraken Javascript benchmark (lower is better):
Chrome 19 2416.8ms
Firefox 12 2112.9ms
WebView 2.2b9 7988.9ms
IE 9.0.6 9403.0ms
Intensive Canvas
Spinning 3D buddha (higher is better):
Chrome 19 60fps
Firefox 12 43fps
IE 9.0.6 16fps
WebView 2.2b9 7fps
JQuery
JQuery test suite execution (lower is better):
Chrome 19 21826ms
WebView 2.2b9 22742ms
Firefox 12 23554ms
IE 9.0.6 28247ms
Based on the above benchmarks (run on my Windows 7 desktop), as long as WebView is stable and functional enough for you, then performance of WebView vs other browsers should not be an issue (as long as your app does not feature a lot of 3D spinning buddhas . . . :-).
Update
As uta's answer states, the JavaScript JIT compiler is switched on for the Win 32 bit build of JavaFX 2.2 and off for the Win 64 bit build of JavaFX 2.2. This means that WebView JavaScript benchmarks are significantly slower (typically 4 to 5 times slower) when running the 64 bit JavaFX version vs the 32 bit JavaFX version.