The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guill ´en, Nielsen and P´erez-Mar´ın, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this paper the efficiency performance of these two estimators when applied to real survival data are compared. Our results suggest that the efficiency improvement introduced by the naive local constant estimator is highly remarkable for all distribution quantiles, especially for low quantiles.