Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently encode such complex spatial priors, thereby, allowing for a strong model dimensionality reduction that comes at the price of enhanced non-linearity. In this setting, we explore a recent adaptive sequential Monte Carlo (ASMC) approach that builds on annealed importance sampling (AIS); a method that provides both the posterior probability density function (PDF) and the evidence (a central quantity for Bayesian model selection) through a particle approximation. Both techniques are well suited to parallel computation and rely on importance sampling over a sequence of intermediate distributions, linking the prior and the posterior PDF. Each subsequent distribution is approximated by updating the particle weights and states, compared with the previous approximation, using a small pre-defined number of Markov chain Monte Carlo (MCMC) proposal steps. Compared with AIS, the ASMC method adaptively tunes the tempering between neighboring distributions and performs resampling of particles when the variance of the particle weights becomes too large. We evaluate ASMC using two different conceptual models and associated synthetic cross-hole ground penetrating radar tomography data. For the most challenging test case, we find that the ASMC method is faster and more reliable in locating the posterior PDF than state-of-the-art adaptive MCMC. The evidence estimates are found to be robust with respect to the choice of ASMC algorithmic variables and much less sensitive to the model proposal type than MCMC. The variance of the evidence estimates are best estimated by replication of ASMC runs, while approximations based on single runs provide comparable estimates when using a sufficient number of proposal steps in approximating each intermediate distribution.