For our neural simulator, MOOSE, we use GNU Scientific Library (GSL) for random number generation, for solving system of non-linear equations, and for solving ODE system.
Recently I checked the performance of GSL ode solver V/s Boost ode solver; both using Runge-Kutta 4. The boost-odeint outperformed GSL by approximately by a factor of 4. The numerical results were same. Both implementation were compiled with -O3 switch.
Below are the numerical results. In second subplot, a molecule is changing is concentration ( calcium ) and on the top, another molecule is produced (CaMKII). This network has more than 30 reactions and approximately 20 molecules.
GSL took approximately 39 seconds to simulate the system for 1 year. While Boost-odeint took only 8.6 seconds. (This turns out to be a corner case)
Update: If I let both solvers choose the step size by themselves for given accuracy, boost usually outperforms the GSL solver by a factor of 1.2x to 2.9x. These tests were done during development of a signaling network which has many many reactions. Under no circumstances I have tested, BOOSE ODE solver was slower than GSL solver.