The convergence of large language models (LLMs) with 6G networks is fostering a paradigm of autonomous multi-agent cooperation, which in turn is expected to substantially increase east-west traffic. Although latent-space interaction mechanisms can enable more efficient collaboration than symbolic natural-language (NL) exchanges, prior work often abstracts away the associated communication overhead under practical wireless constraints. In embodied multi-agent settings, heterogeneous interaction media incur disparate inference and transmission costs, thereby inducing an inherent end-to-end (E2E) latency trade-off. To address this, we propose a joint design that integrates communication-media selection with wireless resource allocation. Through analytical characterization and simulation-based evaluation, we show that neither token-based transmission nor key-value (KV) cache-based transmission is uniformly optimal across operating regimes, as performance depends critically on system parameters such as available computational resources and channel conditions. Accordingly, we formulate a joint optimization problem aimed at minimizing the E2E latency of multi-agent collaboration and develop a low-complexity joint media selection and resource allocation (JMSRA) algorithm. Numerical results further confirm that, by adaptively coordinating the interaction media and bandwidth allocation over heterogeneous links, the proposed scheme achieves markedly reduced E2E latency relative to conventional NL-only and KV-cache-only baselines, enabling efficient and robust multi-agent collaboration in future wireless networks.