Innovative and multifunctional building materials with low embodied energy and reduced CO2 emissions have attracted considerable attention. Herein, a comprehensive comparison between the use of cork and commercial synthetic aggregates (expanded vermiculite, expanded polystyrene (EPS), and lightweight expanded clay (Leca®)) in the production of geopolymer composites was performed. Additionally, composites containing rubber coming from the recycling of end-of-life tires were also studied. The impact of the aggregate nature and amount on the geometric density, compressive strength, thermal conductivity, sound absorption coefficient, and thermal stability of the composites was evaluated. This investigation demonstrates the feasibility of tuning the geopolymer composites properties according to the envisioned application, cork-composites being the most suitable approach for sound absorbing panels (α = 0.8, 2000single bond3150 Hz), while Leca® and expanded vermiculite containing composites are the best option when considering fire resistant applications.