In this comparative study, we examine the influence of two different FEM discretization techniques (conforming $Q_2/P_1$, nonconforming $/tilde{Q}_1/Q_0$ elements) and solution procedures (various nonlinear Newton variants and multigrid vs./ Krylov-space solvers for the linear subproblems) onto the approximation properties and particularly the total efficiency of corresponding simulation tools for incompressible fluids. We discuss algorithmic details and give numerical results for laminar incompressible flow examples including newtonian and non-newtonian behaviour of {/em Power Law} type.