Cross-lingual transfer-learning is widely used in Event Extraction for low-resource languages and involves a Multilingual Language Model that is trained in a source language and applied to the target language. This paper studies whether the typological similarity between source and target languages impacts the performance of cross-lingual transfer, an under-explored topic. We first focus on Basque as the target language, which is an ideal target language because it is typologically different from surrounding languages. Our experiments on three Event Extraction tasks show that the shared linguistic characteristic between source and target languages does have an impact on transfer quality. Further analysis of 72 language pairs reveals that for tasks that involve token classification such as entity and event trigger identification, common writing script and morphological features produce higher quality cross-lingual transfer. In contrast, for tasks involving structural prediction like argument extraction, common word order is the most relevant feature. In addition, we show that when increasing the training size, not all the languages scale in the same way in the cross-lingual setting. To perform the experiments we introduce EusIE, an event extraction dataset for Basque, which follows the Multilingual Event Extraction dataset (MEE). The dataset and code are publicly available.