This paper proposes and compares different approaches within the general fixed-point framework that allows to deal with multi-user (stochastic) equilibrium assignment with variable demand (VD). The aim was threefold: (i) compare the efficiency and the effectiveness of the internal and the external approaches to stochastic equilibrium assignment with VD; (ii) investigate the efficiency and the effectiveness of different algorithms based on the method of successive averages and its extensions; (iii) investigate the effects of different averaging schemes, different convergence criteria and different path choice models, such as Multinomial Logit model, C-Logit model and Multinomial Probit model. Analyses were carried out with respect to a real network and considering different indicators of both efficiency and effectiveness