How much faster is “D-Wave Two” compared to its predecessor?

I don't have any specific task or algorithm in mind, so depending on how they were tested – Is there any research which shows just how the D-Wave Two computer was faster (in terms of computation performance) than its predecessor (D-Wave One)?

As far as I know the closest answer to your question for applications is given in the recent (still unpublished) work presented at the March meeting by Bibek Pokharel, where he compares graph 3-coloring instances on D-Wave Two, D-Wave 2X and D-Wave 2000Q, all other things staying reasonably equal. The short answer is that all the performance increase is essentially due to the possibility to run single anneals at shorter anneal-time. (e.g. 1$\mu$s instead of 5$\mu$s gives indeed about 5X of performance increase, in terms of time-to-solution (TTS) metric. With respect to 20$\mu$s of D-Wave Two the scaling is different).