Numerical simulation of stiff and hybrid systems is widely used in various engineering domains. Numerical solvers, originally designed for purely continuous problems, are not sufficient for these systems. Modern simulation environments provide necessary modifications and extensions to solve the problem. The implementation details of solvers and run time systems greatly affect the performance of simulations regarding accuracy, velocity of simulation, compactness of results, and efficiency. Since no all-powerful solver exists, we assess four popular solvers (DASSL, LSODAR, DOPRI5, RADAU IIA), included in the all-purpose simulator Dymola® for different problems with continuous, stiff, and hybrid behavior. Key traits, including the number of steps, accuracy, CPU time and the event handling capability, are examined and advice for solver selection is given.