Benchmarking Windows Phone devices remains a challenge. Benchmark suites like GLBenchmark and Geekbench that work in iOS and Android are not (yet) available for Windows Phone. Because of this it's difficult to compare Windows Phones with other phones. The only benchmark that does work on all three OS is the one that tests the browsers, but that only tells parts of the story.
The browser benchmarks that we use give a mixed picture. Browsermark (recently updated and only run on the HTC 8X) shows that the Windows Phone 8 devices can't keep up with the iPhone 5 and recent Android phones. This is reiterated by Peacekeeper. Sunspider, on the other hand, works like a charm on Internet Explorer for Windows Phone 8.
When we compared both phones with WPbench, a benchmark made for Windows Phone 7 that tests CPU, GPU and memory speed, it turns out that both are about equally fast, and quite a bit faster than older Windows Phone 7.5 devices.