The benefits of an information ecosystem based on social media platforms came at the cost of the rise of several antisocial behaviours, including the use of toxic speech. To assess the aspects that concur with the formation of toxic conversations, we provide a multi-platform comparison on Twitter and YouTube between the 2022 Italian Political Elections, representing a potentially polarising topic, and the Italian Football League, a topic close to the country's popular culture. We first probe structural and conversational toxicity differences by analyzing 257K conversations (3.7M posts, 1M users) on both platforms. Then, we provide a machine learning approach that, by leveraging the previous features, identifies the presence of the following toxic comment in different stages of conversations. We show that football tends to exhibit lower toxicity levels than politics, with the latter producing more extended conversations that attract a broader audience and consequently fostering the polarization phenomenon. The implemented classifiers resulting from the conversation stage-based approach achieve state-of-the-art performances despite a restricted set of features. Furthermore, our cross-topic comparison shows that models trained on a divisive topic can be applied to other discussions without causing a degradation of their performance.