It's mostly an issue of what describes your data best.
If you have a categorical predictor in your model that you are trying to model (e.g., 1 or more treaments versus contol) and a well balanced set of other covariates, you can get an idea of which is better by doing some simple plots. If you plot survival versus the log of time for the groups and the survival curves in that scale are reasonably evenly spaced in the horizontal (log-time) direction, then that's consistent with an AFT model's acceleration of time. If you plot the log of the cumulative hazard versus time for the groups and the curves are reasonably evenly spaced in the vertical (log-cumulative-hazard) direction, then that's consistent with proportional hazards (PH).
Things are trickier to plot if you are modeling continuous covariates, but the basic principles are the same. For example, you can fit a Cox semi-parametric PH survival model to the data and use scaled Schoenfeld residuals to evaluate whether the association of the predictor with outcome is relatively constant over time. Several chapters of Frank Harrell's Regression Modeling Strategies discuss survival modeling, with examples of the types of diagnostic plots that you can use to evaluate how well either an AFT or a PH model work.