Boils down to what your specific goals are in training. If it's for sport, competition, socialization etc then the bulk of available TKD is sufficient. If SD is your goal then you'll need to seek out (unless you've already found it at your current school) a TKD school that focuses on SD. And I mean real SD and not a sport-TKD school that just pays lip service to SD or has a SD sign above the trophy case. SD is it's own unique animal and the training/teaching methodology is quite different from the typical sport focuses arts.
Judo is sport. It was designed to be sport. According to Pat 'Dermott' O'Neill who was in his era the highest ranked non-Japanese Judo player in the world...Judo is useless unless the enemy is wearing a Gi.
As far as Japanese Ju Jutsu or any other martial art for that matter it is the same as the TKD statement I made above. What is the focus of the school in question? And more importantly, what is the level of experience of the instructor? An instructor that is a sports champion isn't necessarily a good teacher of SD in the same vein as an instructor of good, solid SD is not necessarily a good teacher for competitions.
So in short, base your questions on what experience your instructor has, the focus of the school and the methodology of instruction.
Qualifications of self-defense?
Self-defense training methodology
Martial Warrior - Self-defense