Dense retrieval models have become a standard for state-of-the-art information retrieval. However, their high-dimensional, high-precision (float32) vector embeddings create significant storage and memory challenges for real-world deployment. To address this, we conduct a rigorous empirical study on the BEIR SciFact benchmark, evaluating the trade-offs between two primary compression strategies: (1) Dimensionality Reduction via deep Autoencoders (AE), reducing original 384-dim vectors to latent spaces from 384 down to 12, and (2) Precision Reduction via Quantization (float16, int8, and binary). We systematically compare each method by measuring the "performance loss" (or gain) relative to a float32 baseline across a full suite of retrieval metrics (NDCG, MAP, MRR, Recall, Precision) at various k cutoffs. Our results show that int8 scalar quantization provides the most effective "sweet spot," achieving a 4x compression with a negligible [~1-2%] drop in nDCG@10. In contrast, Autoencoders show a graceful degradation but suffer a more significant performance loss at equivalent 4x compression ratios (AE-96). binary quantization was found to be unsuitable for this task due to catastrophic performance drops. This work provides a practical guide for deploying efficient, high-performance retrieval systems.