This paper presents a comparative analysis of two state of the art Greek to English machine translation systems, ChatGPT-4 (paid version) and Gemini, focusing on their ability to handle specific linguistic phenomena. The phenomena under scrutiny include ambiguity, long sentences, modal verbs, idiomatic expressions, negations, and compositionality. By translating a carefully selected dataset from Greek to English, we evaluate the performance of both systems based on their ability to preserve meaning and produce grammatically correct translations. The results show significant differences between the way the two systems handle complex sentence structures and subtle contextual differences. Furthermore, we examine the strengths and weaknesses the two systems present in accuracy, fluency and overall quality. The study provides useful insights into how reliable modern machine translation systems are by exploring their strengths and limitations. The persuasiveness of these systems was tested in addressing various linguistic challenges and the paper suggests potential improvements for managing complex language patterns more accurately. These findings contribute to the on-going discussion about refining translation technologies for more practical and accurate real-world applications.