Tannin-based foams have gained attention as a potential bio-based alternative to conventional synthetic foams. Traditionally, namely condensed tannins (CT) have been used, leaving the potential of hydrolysable tannins (HT) largely unexplored. This study compared the performance of chestnut (HT) and quebracho (CT) in tannin–protein-based foams at different tannin ratios. Using soy protein isolate (SPI) and hexamine under acidic conditions, a series of tannin foams were produced through a mechanical foaming method and analyzed for cell structure, compression strength, thermal conductivity, and chemical stability. Results show that chestnut tannin is viable in hexamine SPI formulations but is harder to process due to lower reactivity, further resulting in higher material densities compared to quebracho. Foams with higher quebracho content featured smaller, more interconnected cells, while increasing chestnut content led to larger, less interconnected cells. Compression strength decreased with higher chestnut content, while fire resistance and thermal conductivity were influenced by material density rather than tannin type. The 13C-NMR analysis revealed covalent bonding of hexamine with both tannins, but potential covalent bonds with SPI were undetectable. Overall, chestnut tannin can substitute quebracho tannin in hexamine-SPI foams, though with compromises in terms of specific material properties and processability.