Here is a demo of the difference in computing efficiency between Gauss 10 and Gauss 13. The sample codes for this comparison is available at Heer and Maussner's website that is a supplement for their computational economics textbook, "Dynamic general equilibrium modeling." The sample file run in this experiment is named Rch91d.g. The goal of the computations is for obtaining the steady state asset holdings distribution across cohorts of a simple Auerbach-and-kotlikoff type large scale overlapping generation (OLG) model based on a gradient quasi-Newton method with BFGS algorithm for approximating the estimated inverse Jacobian matrix.
As seen in the figure below, Gauss 13 is a tad faster than Gauss 10 by 0.04 seconds in this experiment. In addition to the speed, it seems to me that Gauss 13 provides better interfaces for debugging, variable watching, and data browsing.