Two haloargentate hybrids, [Me-dabco]Ag2X3 (Me-dabco = 1-methyl-1,4-diazabicyclo-[2.2.2]octan-1-ium, X = I (1) or Br (2)), with the same formula but different structures have been synthesized by a slow evaporation method and characterized by microanalysis, infrared spectroscopy, thermogravimetric, and powder X-ray diffraction techniques. Hybrid 1 consists of completely isolated [Ag4I6]2- clusters, while hybrid 2 exhibits a complicated one-dimensional (1D) chain structure formed by four different configurations of neutral chains and two dissimilar configurations of anionic chains. Hybrid 2 undergoes two reversible order-disorder phase transitions, while hybrid 1 displays one reversible and one irreversible structural phase transition. Both 1 and 2 displayed step-like dielectric anomalies in the vicinity of the phase transition temperature. The corresponding dielectric constants in the high dielectric states are approximately 13 and 6 times higher than those in the low dielectric states for 1 and 2, respectively. Interestingly, the subtle change of halides from I- to Br- significantly affects the aggregated structure of haloargentate, the phase transition, and dielectric behaviors, revealing the typical 'butterfly effect' with the ion radii of halides in these two haloargentate hybrids.