Pseudomonas aeruginosa poses major public health threats, due to its robust, treatment-resistant biofilms, which contribute to multi-drug resistance. Bacteriophages offer a promising alternative. This study evaluates giant Phikzvirus and conventional Pbunavirus phages against pre-formed biofilms from four multi-drug-resistant P. aeruginosa clinical isolates. We tested six phages (three Phikzvirus, three Pbunavirus) against four clinical strains, isolated from chronic urological and pulmonary infections (Ur1, Ur14, Lu3, Lu9) at MOIs 0.001–0.1, quantifying biofilm biomass by crystal violet and visualizing architecture by SEM. Phage treatment leads to significant disrupted biofilms in three isolates achieving more than 50% reduction—comparable with typical antibiotic efficacy against mature biofilms. All biofilms retained their EPS architecture after the treatment, as revealed by SEM, suggesting that residual eDNA-polysaccharide complexes could maintain structural cohesion even after bacterial lysis. The phage’s ability to reduce biofilm biomass demonstrated a significant dependence on the multiplicity of infection (MOI). The best results of anti-biofilm activity of phages (reduction in biofilm biomass by more than 75%) were observed for the phage phiKZ for two strains—Ur1 at MOI = 0.001 and Lu9 at MOI = 0.01—and for the phage phi14/1 for the Ur1 strain at MOI = 0.001. The biofilm formed by the antibiotic-resistant clinical isolate Ur14 demonstrated exceptional resistance to both types of bacteriophages despite the sensitivity of bacteria of this strain to the studied phages. This highlights the need for personalized phage therapy, where tailored phage cocktails are selected for each specific bacterial strain to achieve optimal destruction of the biofilm.