Downstream processing of machine translation (MT) output promises to be a solution to improve translation quality, especially when the MT system's internal decoding process is not accessible. Both rule-based and statistical automatic post-editing (APE) methods have been proposed over the years, but with contrasting results. A missing aspect in previous evaluations is the assessment of different methods: i) under comparable conditions, and ii) on different language pairs featuring variable levels of MT quality. Focusing on statistical APE methods (more portable across languages), we propose the first systematic analysis of two approaches. To understand their potential, we compare them in the same conditions over six language pairs having English as source. Our results evidence consistent improvements on all language pairs, a relation between the extent of the gain and MT output quality, slight but statistically significant performance differences between the two methods, and their possible complementarity.