Personally, I tend to use MiniZinc for prototyping and experimenting and for solving simple problems.
For building larger solutions, I would also probably use a solver directly. Reasons for that would be customization, integration, and data handling issues. For me the go-to system would be Gecode, but there are a lot of very interesting and varied solvers available.
Worth noting is that MiniZinc is starting to get more and more support for integration into large systems, for example with the python interface (https://pypi.org/project/minizinc/).
Basically this for me too; MiniZinc is great whilst you don't really have the full problem nailed, when it's harder to pick what you'd like to focus on using sovler wise.
I use Python to generate DPLL and likewise with MiniZinc. It’s no different from SQL: there’s something of an impedance mismatch that’s already felt in eg Sympy.
Their DSL look very similar to a lot of specific DSLs of other tools in the field
As opposed to OR-Tools where you can directly use a language you know (like Python) to express your constraints and targets
Having worked with both approaches, I like the latter better