We numerically investigate and compare the performance of modulation format independent carrier phase esti- mation (CPE) (or universal CPE (U-CPE)) and decision directed CPE (DD-CPE) along with digital backward propagation (DBP) to compensate fiber non-linearity, for polarization multiplexed (PM) 4 and 16-ary quadrature amplitude modulation (QAM) coherent systems. We analyze the impact of each of the CPE methods in reducing the complexity of DBP, in terms of required DBP steps, as well as the influence of the laser line width effects on their performance. By optimizing the step size, the U-CPE method, in spite of its low complexity, exhibits a similar performance as the DD-CPE method in non-linearity mitigation. However, at high signal launch powers, and in the presence of laser phase noise, the performance of DD-CPE method is significantly impaired owing to increased erroneous pre-decisions, whereas, the U-CPE method is still capable of mitigating both non-linearity and phase noise, equivalently good as the ideal DD-CPE case. Moreover, also without DBP for non-linear compensation, U-CPE method outperforms the DD-CPE method allowing high signal launch powers and with greater tolerance towards phase noise.