Turing has more things that work out of the box, so if you do not have complex requirements its a good first step. Gen allows for composing models using its generative function interface, you can specify models in different ways. You can also have fine grained control over inference, rather than a few preset methods. Gen has also worse error messages and docs.

From the Gen leads Marco and Alex: https://discourse.julialang.org/t/whats-the-difference-betwe...