There is no difference whatsoever between the GPL and the AGPL for software you distribute.
The only difference between the AGPL and the GPL relates to software you don't distribute, but that you make available over a network, such as hosting an AGPL web server. The AGPL says that as long as public users interact with this web server, they have the right to get the code and deployment instructions and AGPL rights to be able to run the exact same service themselves, just as if they had downloaded the software.
The FSF's (very reasonable) position is that linking to a piece of software makes your software a derivative work, but that launching it as a separate process or accessing it over a network generally doesn't. However, if you exchange very complex internal data structures with this GPL software running in a separate process, whether you do it over a network or through pipes or command line arguments or whatever, then your program is still a derivative work, in their opinion.
That is, if you run gcc in a separate process but then mmap() it's memory and search for its entry points and jump to the memory locations of GCC functions in order to generate optimized code for a piece of GCC AST you provide, then your program is a derivative of GCC (according to the FSF, at least) even though GCC is running in a separate process.