Two packing problems are considered in this paper, namely the well-known strip packing problem (SPP) and the variable-sized bin packing problem (VSBPP). A total of 252 strip packing heuristics (and variations thereof) from the literature, as well as novel heuristics proposed by the authors, are compared statistically by means of 1170 SPP benchmark instances in order to identify the best heuristics in various classes. A combination of new heuristics with a new sorting method yields the best results. These heuristics are combined with a previous heuristic for the VSBPP by the authors to find good feasible solutions to 1357 VSBPP benchmark instances. This is the largest statistical comparison of algorithms for the SPP and the VSBPP to the best knowledge of the authors.