This paper analyzes the performance of Small Language Models (SLMs) and Vision Language Models (VLMs) and evaluates the trade-off between model performance and carbon emissions across 4 essential tasks: Image Captioning, Visual Question Answering (VQA), Dialogue Summarization and Text-to-SQL conversion. Various SLMs and VLMs belonging to the Qwen and LLaMA architecture family are chosen and variants based on model size in terms of the number of parameters, quantization level and fine-tuning parameters are evaluated. The model variant's performance and carbon emissions are calculated. To quantify the trade-off between model performance and carbon emissions, we introduce a novel metric called CEGI (Carbon Efficient Gain Index). This metric represents the carbon emission per unit percentage gain per million trainable parameters . This metric provides a normalized measure to compare model's efficiency in terms of performance improvement relative to their environmental cost. The experiment's outcome demonstrates that fine-tuning SLMs and VLMs can achieve performance levels comparable to Large Language Models (LLMs) while producing significantly less carbon emissions. Our findings suggest that the marginal gains in accuracy from larger models do not justify the substantial increase in carbon emissions. Leveraging lower-bit quantization levels, the proposed metric further enhances energy efficiency without compromising performance. This study highlights balancing high performance and environmental sustainability. It offers a valuable metric for selecting models suitable for environmentally-friendly AI development.