Thanks for the question. Indeed, Rimu.jl is using a stochastic power method, which is quite different from path integral QMC.
There are a number of reasons why we chose to go with Julia. No, Rimu.jl does not rely on differential equation solvers. Many good reasons (as in this post) we only discovered later. At the time it was just the appeal of having a modern high-level language with easy-to-read syntax and access to plotting, scripting, etc, while being able to write fast and generic code. We wanted to keep the code flexible such that we could experiment easily with different algorithms, and different physics problems. We had the option of diving into an existing Fortran code base that was written and optimised for quantum chemistry, and extending it to do the things we wanted (bosons, mixtures with different spin flavours), which seemed really hard. Writing a new code in Julia seemed much more fun. And it was!