In the hybrid closed-loop supply chain (CLSC) with diverse collectors, customers increasingly prioritize the convenience in returning end-of-life (EOL) products. This trend necessitates supply chain entities to enhance their collection service to address the intensifying competition for EOL products collection. To devise appropriate convenience and pricing strategies, we construct a hybrid game-theoretic CLSC model encompassing a manufacturer, a retailer, and a third-party collector, and we propose new collection functions that cater to varying levels of collection competition, spanning monopoly, duopoly, and hybrid competitive scenarios. Furthermore, we delve into the influence of customers' preferences or distrust towards a specific collector on the collection competition, which is caused by factors such as more convenient offline stores or unqualified recycling process. Our study first reveals that collection competition is affected by all collectors' convenience strategies, while the total collection rate is dominated by the most preferred collectors' convenience strategy. Second, both customer's preference and distrust negatively affect pricing and convenience strategies, albeit with differing effects on collection rates across various competition levels. Notably, channel distrust exerts a more substantial influence on manufacturers' and third-party collectors' strategies. Third, we also examine how competitive collection and customer behavior shape the proportion of collected products destined for different recovery options, i.e., remanufacturing and recycling, as well as the overall efficiency of recovering collected products across the entire supply chain. And channel preference plays a more positive role in enhancing the overall collection rate for the supply chain.