Aspect-based Sentiment Analysis (ABSA) extracts fine-grained opinions toward specific aspects within text but remains largely English-focused despite major advances in transformer-based and instruction-tuned models. This work presents a multilingual evaluation of state-of-the-art ABSA approaches across seven languages and four subtasks (ACD, ACSA, TASD, ASQP). We systematically compare different transformer architectures under zero-resource, data-only, and full-resource settings, using cross-lingual transfer, code-switching and machine translation. Fine-tuned Large Language Models (LLMs) achieve the highest overall scores, particularly in complex generative tasks, while few-shot counterparts approach this performance in simpler setups, where smaller encoder models also remain competitive. Cross-lingual training on multiple non-target languages yields the strongest transfer for fine-tuned LLMs, while smaller encoder or seq-to-seq models benefit most from code-switching, highlighting architecture-specific strategies for multilingual ABSA. We further contribute two new German datasets, an adapted GERestaurant and the first German ASQP dataset (GERest), to encourage multilingual ABSA research beyond English.