In many industrial processes, the collisions of droplets play a vital role in their performance. The fluids encountered in these applications often exhibit non-Newtonian behavior. These effects have a large effect on the outcome of the process and are currently not fully understood. To gain further knowledge, numerical simulations are performed using the Volume of Fluid Method and the Local Front Reconstruction Method. The non-Newtonian behavior exhibited by the droplets is the Ostwald-de Waele equation, including both shear-thinning and shear-thickening behavior. Earlier work shows this numerical setup is well equipped to simulate reality based on comparison with experiments for Xantham gum. The droplet collisions are performed until Weber numbers 300 for both head-on and off-center collisions. The rheology ranges from shear-thinning (n=0.5) to shear-thickening (n=2). For collisions at low Weber numbers, both simulation methods produce similar outcomes, whereas at higher Weber numbers the disintegration of the droplets follows a different mechanism, induced by the difference in numerical treatment of both methods. The transitions between the different outcome regimes were shown to be largely dependent on the power-law index. Our results further show that the expansion of the ring and the related diameter increases for higher Weber number and decreasing power-law index. In the case of off-center collisions, the detachment of the ligament is delayed for increasing Weber numbers and more shear-thickening fluids. This is accompanied by a higher critical ligament length. The results show there is a significant difference in collision dynamics for shear-thickening and shear-thinning fluids.