Thanks for reading. That's a good question. Here are some thoughts.

At a high level these are different approaches to doing the same thing, so in many situations both will work fine.

The propensity score based methods are more reminiscent of RCT where there is a clear treatment and control group (e.g. pill or no pill groups), so they work well in these types of contexts.

Regression based approaches also work well here. However, regression based methods typically spit out a model for the causal connections between variables (as opposed to just average causal effects) which can help with more detailed predictions/simulations and gaining a deeper understanding of the system of interest.