For everything else regarding concurrent access to shared data out of process, they are on the same foot.
Ada didn't took off, because of several reasons, price of compilers, on UNIX it was an additional SKU on top of the respective developers SDK that already offered C and C++ in the box, 1980's mainstream hardware wasn't able to cope with it, most OS vendors outside UNIX decide to migrate from their toolchains into C and C++, so again additional money on top of the OS SDK.
Early Ada compilers had expensive licensing and required expensive hardware to run.
By the time GNAT was added to GCC, C++ had already taken over most of the spaces that were not Ada exclusive (meaning safety critical / defense / aerospace niches where either Ada was once mandated or has thrived in despite the original high costs).