This paper presents the results of a comparison of the well-established power-flow algorithms Gauss-Seidel, Newton-Raphson, Dishonest Newton-Raphson, Decoupled Load Flow, Fast Decoupled Load Flow, DC Power-Flow and the new Holomorphic Embedding Load Flow Method (HELM). The algorithms are assessed using 21 PQ-powerflow test cases with numbers of nodes ranging from 2 to 3120. The focus of the analysis is on the precision of the solutions of the algorithms and the required computation time. The comparison shows some disadvantages of HELM and motivates a new Adaptive Hybrid Approach that combines the Holomorphic Embedding Load Flow Method and iterative algorithms to merge the benefits of both techniques. The Adaptive Hybrid Approach is able to calculate precise solutions for every test case without starting values and is on average faster than the Newton-Raphson method while being more flexible than every other algorithm considered here. It is also shown that the Adaptive Hybrid Approach yields the correct solution like HELM if it exists.