Falls are one of the leading causes of mortality among the older population, being the rapid detection of a fall a key factor to mitigate its main adverse health consequences. In this context, several authors have conducted studies on acceleration-based fall detection using external accelerometers or smartphones. The published detection rates are diverse, sometimes close to a perfect detector. This divergence may be explained by the difficulties in comparing different fall detection studies in a fair play since each study uses its own dataset obtained under different conditions. In this regard, several datasets have been made publicly available recently. This paper presents a comparison, to the best of our knowledge for the first time, of these public fall detection datasets in order to determine whether they have an influence on the declared performances. Using two different detection algorithms, the study shows that the performances of the fall detection techniques are affected, to a greater or lesser extent, by the specific datasets used to validate them. We have also found large differences in the generalization capability of a fall detector depending on the dataset used for training. In fact, the performance decreases dramatically when the algorithms are tested on a dataset different from the one used for training. Other characteristics of the datasets like the number of training samples also have an influence on the performance while algorithms seem less sensitive to the sampling frequency or the acceleration range.