Are there performance differences amongst the different Gurobi APIs?

The Gurobi APIs (Java, Python, C++, C#, R, and Matlab) are thin layers built on top of the C API. These APIs collect the data and pass it on to the core library, which is written in C. From a solver and solving performance point of view, there is no difference between, for example, Python and Java.

However, the API can make a difference for the model building part of the code. Model building is in the chosen language and depends on the user's proficiency of the language, the data structures that are used, and how fast the language is.