Recently, the authors have developed a method for real-time dynamics of multibody systems, which combines a semi-recursive formulation to derive the equations of motion in dependent relative coordinates, along with an augmented Lagrangian technique to impose the loop closure conditions. The following numerical integration procedures, which can be grouped into the so-called structural integrators, were tested : trapezoidal rule, Newmark dissipative schemes, HHT rule, and the Generalized-${alpha}$ family. It was shown that, for large multi body systems, Newmark dissipative was the best election since, provided that the adequate parameters were chosen, excellent behavior was achieved in terms of efficiency and robustness with acceptable levels of accuracy. In the present paper, the performance of the described method in combination with another group of integrators, the Implicit Runge-Kutta family (IRK), is analyzed. The purpose is to clarify which kind of IRK algorithms can be more suitable for real-time applications, and to see whether they can be competitive with the already tested structural family of integrators. The final objective of the work is to provide some practical criteria for those interested in achieving real-time performance for large and complex multibody systems.