We establish an approach to measure the nonclassicality of a two-mode quantum state by extending the method of quantifying nonclassicality for a single-mode quantum state. We then discuss the nonclassicality and entanglement properties of several different quantum states, and determine the optimal phase estimation for entangled coherent states (ecs) in the form of nonclassicality and concurrence. Accordingly, a new interferometer (linear and nonlinear) scheme is proposed by modifying a traditional interferometer. Specially, we specify a new normal ordering form of the evolution operator of nonlinear interferometer (NI) using the techniques of integration within an ordered product of operators (IWOP), and obtain the parity signal based on representation of the coherent state. By inputting several common quantum states, we further study the phase sensitivity of the linear interferometer (LI) and NI with parity detection, and perform a detailed comparison among the different input states schemes. Furthermore, we quantitatively investigated the effect of nonclassicality and entanglement on the phase sensitivity of two interferometers. These results show that nonclassicality or entanglement is very crucial but not a necessary condition for improving the phase sensitivity of interferometers.