Even though some parts of the refinement are done in parallel on multiple processors, the really time-consuming calculations are done in serial, which ends up governing the overall speed of the process.
I have found that Intel Haswell-class processors like the Core i7 4770 perform refinements significantly speedier than our brand new 12-core Xeon server that is less than 6 months old. So it is my naive guess that getting the fastest "single processor performance" will get you maximal refinement speeds on PHENIX.
Cheers, Jim