The detection and characterization of bursting activity remains a topic where no consensual definition has been reached so far. We compare here three different approaches of spike trains variability: statistical characterization (average frequency, coefficient of variation), burst detection (Poisson and rank surprise) and multi-scale analysis (detrended fluctuations analysis). Using both real and simulated data, we show that Poisson surprise provides information closely related to the coefficient of variation and that rank surprise detects significant bursts which are associated with long-range correlations. Since these long-range correlations are only adequately characterized with multi-scale analysis, this study emphasizes the complementarity of these approaches for the complete characterization of spike trains.