Viscoelastic properties of soft substrates play a crucial role in the evaporation dynamics of sessile drops. Recent studies have revealed that the modification of the viscoelastic properties of substrates changes the dynamics of the three-phase contact line, consequently affecting the evaporation behavior of sessile drops. Notably, these modifications occur without any noticeable changes to the substrate's wetting characteristics or surface topography. However, the individual role of storage (G′) and loss (G″) moduli of substrates on drop evaporation dynamics remains unexplored. In this study, we investigate the evaporation dynamics of water drops on two groups of poly(dimethylsiloxane)-based viscoelastic substrates possessing either identical G′ with varying G″ or identical G″ with varying G′. Our study reveals that on a substrate with constant shear modulus (G′), a reduction of an order of magnitude in loss modulus shifts the evaporation process from the constant contact radius mode to the constant contact angle mode. We hypothesize that this observed shift in behavior stems from the varying viscoelastic dissipation influenced by the plateau modulus and characteristic relaxation time of polymer gels. Our hypothesis is further supported from the observation that the evaporation process persists on the substrate with constant loss modulus (G″). Our study advances the current understanding of drop evaporation on soft substrates that may find potential applications involving soft composites, biological entities, tissue engineering, and wearable electronics.