Aspect-based Sentiment Analysis (ABSA) helps to explain customers' opinions towards products and services. In the past, ABSA models were discriminative, but more recently generative models have been used to generate aspects and polarities directly from text. In contrast, discriminative models commonly first select aspects from the text, and then classify the aspect's polarity. Previous results showed that generative models outperform discriminative models on several English ABSA datasets. Here, we evaluate and contrast two state-of-the-art discriminative and generative models in several settings: cross-lingual, cross-domain, and cross-lingual and domain, to understand generalizability in settings other than English mono-lingual in-domain. Our more thorough evaluation shows that, contrary to previous studies, discriminative models can still outperform generative models in almost all settings.