Brancher is targeted to a wider audience, including people who have only a basic training in machine learning and Python programming. The interface is designed to be as close as possible to the math. The downside is that Brancher is less flexible than Pyro.
Hi. The main difference with PyMC is that Brancher is build on the top of the deep learning library PyTorch. Every deep learning tool that is implemented in PyTorch can be used for constructing deep probabilistic models in Brancher.
Also PyMC mostly uses sampling while Brancher is based on variational inference.