The design of multifunctional hydrogels based on bioactive hyaluronic acid (HA) and antibacterial cationic polymer ɛ-poly-l-lysine (ε-PL) is a promising tool in tissue engineering applications. In the current study, we have designed hyaluronic acid and ɛ-polylysine composite hydrogel systems with antibacterial and cell attractive properties. Two distinct crosslinking approaches were used: the physical crosslinking based on electrostatic attractions and the chemical crosslinking of charged functional groups (-NH2 and -COOH). The impact of the crosslinking strategy on fabricated hydrogel molecular structure, swelling behavior, gel fraction, morphology, porosity, viscoelastic properties, antibacterial activity, and in vitro biocompatibility was evaluated. Both chemically and physically crosslinked HA/ԑ-PL hydrogels demonstrated fast swelling behavior and long-term stability for at least 28 days, as well as similar order of stiffness (10–30 kPa). We demonstrated that physically crosslinked hydrogels inhibited over 99.999% of Gram-negative E. coli, while chemically crosslinking strategy led to the antibacterial efficiency decrease. However, cell viability was significantly improved, confirming the importance of the applied crosslinking approach to the antibacterial activity and in vitro biocompatibility. The distinct differences in the physicochemical and biological properties of the developed materials provide new opportunities to design next-generation functional composite hydrogel systems.