For something simple like a counter if multiple threads will be increasing the number. I read that mutex locks can decrease efficiency since the threads have to wait. So, to me, an atomic counter would be the most efficient, but I read that internally it is basically a lock? So I guess I'm confused how either could be more efficient than the other.
Atomic operations leverage processor support (compare and swap instructions) and don't use locks at all, whereas locks are more OS-dependent and perform differently on, for example, Win and Linux.
Locks actually suspend thread execution, freeing up cpu resources for other tasks, but incurring in obvious context-switching overhead when stopping/restarting the thread. On the contrary, threads attempting atomic operations don't wait and keep trying until success (so-called busy-waiting), so they don't incur in context-switching overhead, but neither free up cpu resources.
Summing up, in general atomic operations are faster if contention between threads is sufficiently low. You should definitely do benchmarking as there's no other reliable method of knowing what's the lowest overhead between context-switching and busy-waiting.