The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. (2004). The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox (2005) to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver.