We have studied the diamond to β-tin phase transition in Si using diffusion quantum Monte Carlo (DMC) methods. Slater-Jastrow-backflow trial wave functions give lower DMC energies than Slater-Jastrow ones, and backflow slightly favors the β-tin phase with respect to the diamond phase. We have investigated the changes in the equation of state that result from the use of different pseudopotentials, the inclusion of either zero-point motion or finite-temperature vibrations, and the application of corrections for finite-size effects. Our tests indicate that the choice of pseudopotential can significantly affect the equation of state. Using a Dirac-Fock pseudopotential leads to an overestimation of the transition pressure but an empirical pseudopotential designed for use in correlated calculations gives a transition pressure in quite good agreement with experiment.