The author is concerned with the comparison of the solutions of the linear autonomuous functional differential equation \[ x'(t)= Lx_t\tag{*} \] and the perturbed equation \[ x'(t)= Lx_t+ f(t, x_t),\text{ where }f: [\sigma_0,\infty)\times \mathbb{C}\to \mathbb{C}^n\tag{**} \] is a continuous function and \(x_t\) is defined by \(x_t(s)= x(t+ s)\) for \(-r\leq s\leq 0\). The present paper is the continuation of the author's results in [J. Math. Anal. Appl. 316, No. 1, 24--41 (2006; Zbl 1102.34060)].