We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we prove that the error of its solution to the original solution is of order 1/2.