Human similarity and relatedness judgements between concepts underlie most of cognitive capabilities, such as categorisation, memory, decision-making and reasoning. For this reason, the proposal of methods for the estimation of the degree of similarity and relatedness between words and concepts has been a very active line of research in the fields of artificial intelligence, information retrieval and natural language processing among others. Main approaches proposed in the literature can be categorised in two large families as follows: (1) Ontology-based semantic similarity Measures (OM) and (2) distributional measures whose most recent and successful methods are based on Word Embedding (WE) models. However, the lack of a deep analysis of both families of methods slows down the advance of this line of research and its applications. This work introduces the largest, reproducible and detailed experimental survey of OM measures and WE models reported in the literature which is based on the evaluation of both families of methods on a same software platform, with the aim of elucidating what is the state of the problem. We show that WE models which combine distributional and ontology-based information get the best results, and in addition, we show for the first time that a simple average of two best performing WE models with other ontology-based measures or WE models is able to improve the state of the art by a large margin. In addition, we provide a very detailed reproducibility protocol together with a collection of software tools and datasets as supplementary material to allow the exact replication of our results.