Horseradish peroxidase (HRP)-catalyzed in situ forming hydrogel systems—with their tunable gelation rate and mechanical properties—have wide applications in biomedicine. HRP has moderate substrate specificity that can be tuned easily by changing the precursor reactants, among which phenol-conjugated polymers are the most studied. In this study, we investigated the relationship between the functional groups on the polymer chains and the properties of the crosslinked hydrogels produced by HRP. As phenols and catechols have similar structures, we conjugated 4-arm poly(propylene oxide)-poly(ethylene oxide) (tetronic) derivatives with catecholamine (dopamine hydrochloride, DA) and phenylamine (tyramine, TA). We prepared tetronic-dopamine (TDA) and tetronic-tyramine (TTA) hydrogels by mixing an aqueous solution of TDA and TTA with HRP in the presence of hydrogen peroxide (H2O2) and characterized and systematically compared their gelation properties: gelation rate, mechanical strength, swelling ratio, adhesive strength, and cellular activity. The gelation pathways of TDA and TTA were similar, and their gelation properties were well controlled by varying the HRP and H2O2 concentrations. Despite their similar molecular structures, the TDA hydrogels showed lower crosslinking densities but superior adhesive strength than the TTA hydrogels at the same HRP and H2O2 concentrations. Neither hydrogel showed cytotoxicity toward encapsulated human dermal fibroblast cells.