Judo or BJJ for self-defense might give time to both, plus some work on defending against strikes.
BJJ-for-MMA has little need for judo throws or working gi takedowns, but their wrestling might get a lot of attention. Sport-BJJ views takedowns as optional. Judo can be balanced or it can focus entirely on just surviving groundwork. Judo or BJJ for self-defense might give time to both, plus some work on defending against strikes.