I would argue that a PPL based on programmable inference allows you to more easily implement problem specific inference algorithms. It’s usually more low level, like Gen, and requires more knowledge about Bayesian inference algorithms and PPLs in general.

Compositional inference aims to combine inference algorithms, such that you can use, e.g. HMC, for some set of variables and another inference algorithms for the rest. This is useful for more complex models where you don’t want to write tailored inference algorithms but need the flexibility to combine different algorithms for efficient inference.

Universal probabilistic programming refers to inference in probabilistic programs that contain stochastic control, varying number of parameters and so on. Lots of the more efficient inference algorithms have strong restrictions on the models they can be used for and are not universal, e.g. HMC and VI cannot handle stochastic control flow. For the same reason, you are not able to represent every model that you can write in Turing using a static graph (and need special care for variable name handling) making it impossible to use certain graph based optimisations or inference algorithms. Turing solves that by providing inference algorithms, core routines and data structures that can handle those difficult models.

Which one is faster? This is difficult to say. If you use the same inference algorithms you likely won’t feel any difference. But there are no reliable benchmarks between both. The HMC inference in Turing is comparable to Stan in terms of speed and effectiveness. Don’t know about Gen, but it should be easy to use Turings HMC in Gen if necessary. But because you can more easily implement tailored inference algorithms you might be able to get faster inference for specific models using Gen.

What is easier to use? For general purpose Turing is much easier to use as this is the target audiences. If you want to implement tailored inference algorithms Gen is easier as it is meant for this purpose.