Hybrid search, the integration of lexical and semantic retrieval, has become a cornerstone of modern information retrieval systems, driven by demanding applications like RAG. The design space for these systems is complex, yet a systematic understanding of the trade-offs among their retrieval paradigms, combination schemes, and re-ranking methods is still lacking. To address this, we present the first experimental analysis of advanced hybrid search architectures. Our framework integrates four retrieval paradigms—full-text search, sparse vector search, dense vector search, and tensor search—and evaluates their combinations and re-ranking strategies across 11 real-world datasets. Our results reveal three key findings: (1) A “weakest link” phenomenon, where a weak path can substantially degrade overall accuracy, highlighting the need for path-wise quality assessment before fusion. (2) A data-driven map of performance trade-offs, demonstrating that optimal configurations depend heavily on resource constraints and data characteristics, precluding a one-size-fits-all solution. (3) The identification of tensor-based re-ranking fusion as an alternative to mainstream fusion methods, offering the semantic power of tensor search at a fraction of the computational and memory cost. Our findings offer concrete guidelines for designing adaptive, scalable hybrid search systems and identify key directions for future research.