This paper examines the performance of two Large Language Models (LLMs), GPT3.5 and Llama2 and one Small Language Model (SLM) Gemma, across three different classification tasks within the climate change (CC) and environmental domain. Employing BERT-based models as a baseline, we compare their efficacy against these transformer-based models. Additionally, we assess the models' self-evaluation capabilities by analyzing the calibration of verbalized confidence scores in these text classification tasks. Our findings reveal that while BERT-based models generally outperform both the LLMs and SLM, the performance of the large generative models is still noteworthy. Furthermore, our calibration analysis reveals that although Gemma is well-calibrated in initial tasks, it thereafter produces inconsistent results; Llama is reasonably calibrated, and GPT consistently exhibits strong calibration. Through this research, we aim to contribute to the ongoing discussion on the utility and effectiveness of generative LMs in addressing some of the planet's most urgent issues, highlighting their strengths and limitations in the context of ecology and CC.