In this paper, we present an in-depth comparative analysis of two classifications of argument schemes: Walton's typology and Wagemans' Periodic Table of Arguments. We describe annotation guidelines for each classification and apply these to a corpus of arguments from the 2016 US presidential debates. In so doing, we achieve substantial inter-annotator agreement, and produce what, to the best of our knowledge, are the two largest and most reliably annotated corpora of argument schemes in dialogical argumentation publicly available. In describing the creation and comparison of these corpora, we discuss the strengths of each, with an eye towards both computational modelling and argument mining.