Japanese jiu-jitsu is the samurai battlefield stuff. It is how they defended Japan for over a thousand years from foreign attackers, many of whom were bigger and stronger than the Japanese. It is a quick and brutal style of fighting; they were crotch-kicking long before there was Krav Maga. It is useful against multiple attackers. Everything is designed so that you don't get tied up with an opponent for more than 2-3 seconds. The joint locks are more like a grab and snap kind of thing. Anything you get a hold of, you snap it backwards. They do go to the ground, but it's only for a brief and brutal moment, before standing up to fight the next guy.
The Gracie family invented Brazilian Jiu-Jitsu, by taking out the more brutal moves and adapting the art for fighting on a padded mat. In that scenario, it's much more ok to lay on your back, because unlike either a samurai battle or a street fight, your opponent's friends are not going to walk up behind you and stomp on your head. They also added blood chokes like the triangle choke, which take about 30-60 seconds to make a guy pass out. Once again, useful in a controlled environment, but not so much on a battlefield.
I trained bjj for three years. The best way I can put it is that is the most useful martial art there is...when you are already getting your ass kicked. I know a guy who got beat to death with another dude's bare hands as he sat on his chest. BJJ would have saved his life. When a fight is going poorly, you are going to end up on your back, and bjj is the only system that teaches you to fight from that position. However, as far as putting someone else on their back from standing, collegiate wrestling has superior takedowns to bjj.