For me, the combination of TKD and HKD, as taught at the dojangs where I trained, has worked out great for me.
Before beginning martial art training, I had been in more than a couple scraps. I found my top problems were:
a) closing the gap to get my strikes in without getting hit first
b) generating a powerful strike without telegraphing so it was easily avoided
c) dealing with "wrestlers"
TKD ended up solving the first two fairly quickly. I was fortunate to be training at a time when there were a couple of guys willing to "play rough" but with enough mutual respect and control so we weren't injuring each other.
Specifically, taking hard shots to the side of the face, jaw or forehead can ring the bell (equal to or even exceeding how hard I'd been hit "on the street") but not splattering each other's noses or splitting each other open (er.. there were occassionally cuts... but we made efforts to avoid that kind of contact).
There were times when I was aware that we were dancing on the line between a real fist (and foot

) fight and "sparring." As much intensity and (at times) contact as a real fight was definately there, but the emotion was not. Following the sparring, it was bows and handshakes and smiles.
I learned to get hit HARD and keep my head in the fight. To keep my eyes LOCKED on the opponent, even if getting hit right in the face. To pick my shots and hit them with precision and power — and in combinations of precisely placed strikes.
With FOCUS you can throw everything as hard and fast as you can — you just focus just in front of the surface instead of an inch or two INSIDE, so there is NO "pulling" punches or kicks.
And yes, heavy bags ARE important. I often say some good heavy bag work is some of the best self defense training you can get!
Breaking boards is also a good exercise: you train yourself to short-circuit subconciously "slowing down" strikes at impact so strikes can with hit with penetration at full speed and power.
So did it translate to self defense? You betcha. I've found that it is EASY now to bridge the gap. And as far as power? In the few times I've had to defend myself since training, I've found that very few are used to getting hit as hard as I strike. It usually only takes ONE good shot. And that "good shot" usually is almost always my first strike (the beauty of precision striking...).
As for the third, hapkido (as I've been taught) filled that gap perfectly.
People who have, in the very few times, managed to grab ahold of me regret it.
I by no means believe myself to be "invulnerable," but no martial art training — heck, even a GUN and body armor! — can render you invulnerable.
But the odds have significantly been shifted toward being in my favor.
I make better decisions nowadays and half expect that I may never have to defend myself or a loved one ever again. But should I need to? I feel well prepared. Now it is all about maintaining and honing.