Fiber optical parametric amplifiers (FOPAs) operating based on four-wave mixing (FWM) are versatile devices with increasing applications in optical communication systems. In this paper, the effects of dispersion fluctuations on the performance of bandwidth, ripple, parametric gain, and saturation power of a two-pump FOPA based on four-wave and six-wave models are studied and compared. Coupled-amplitude equations representing the non-degenerate FWM process in optical fiber are solved numerically to compute the parametric gain over the communication wavelengths. The behaviors of the performance parameters are critically analyzed and compared with different types of fluctuation strengths (or amplitudes) specified by the combinations of correlation length (Lc) and fluctuation amplitude (σ). Based on the results, it was found that the flat gain bandwidth for the four-wave model remains unchanged and is insensitive to the strengths of fluctuations. The gain ripples, however, get higher as the fluctuation strengths increase. On the other hand, the flat gain bandwidths of the six-wave model are hardly identified due to the tremendous and continuous ripples within the pump wavelengths. In addition, the minimum parametric gain values for both four-wave and six-wave models reduce as the fluctuation strengths increase. Also, the lowest value of parametric gain leads to the highest saturation power and vice versa. The dispersion fluctuations affect the FWM process's efficiency and deteriorate the overall amplifier performance, particularly for the six-wave model. The numerical analysis obtained via the six-wave model is especially useful since this model closely matches with practical circumstances.