Peer-to-peer live-streaming (P2P-TV) systems' goal is disseminating real-time video content using peer-to-peer technology. Their performance is driven by the overlay topology, i.e., the virtual topology that peers use to exchange video chunks. Several proposals have been made in the past to optimize it, yet few experimental studies have corroborated results. The aim of this paper is to provide a comprehensive experimental comparison based on PeerStreamer in order to benchmark different strategies for the construction and maintenance of the overlay topology in P2P-TV systems. We present only experimental results in which fully distributed strategies are evaluated in both controlled experiments and the Internet using thousands of peers. Results confirm that the topological properties of the overlay have a deep impact on both user quality of experience and network load. Strategies based solely on random peer selection are greatly outperformed by smart yet simple and actually implementable strategies. The most performing strategy we devise guarantees to deliver almost all chunks to all peers with a playout delay as low as 6 s even when system load approaches 1, and in almost adversarial network scenarios. PeerStreamer is open-source to make results reproducible and allow further research by the community.