Automated test case generation remains challenging due to diverse implementation behaviours and complex boundary conditions. This work investigates the effectiveness of Multi-agent Large Language Model (LLM) architectures employing collaborative and competitive interaction patterns, compared against a Single-agent baseline, within the context of black-box testing. Experiments on the HumanEval benchmark show that prompt engineering is the primary driver of performance, with Rule-augmented Few-shot prompting yielding improvements up to 20-30% in both coverage and Execution Success Rate (ESR) against all the other tested strategies — i.e., Zero-shot and conventional Few-shot prompting. Although Multi-agent architectures achieve superior test coverage — peaking at 99.75% — they yield an ESR comparable to Single-agent frameworks (97.31% versus 97.25%). Crucially, this comes at the expense of a threefold to fourfold increase in token expenditure. In contrast, the Single-agent configuration paired with optimised Rule-augmented Few-shot prompting provides the most effective balance between accuracy, coverage, and computational efficiency.