When we’re talking about Jiujitsu as it pertains to fighting there can be only one objective; to win in the most efficient manner possible.
Assuming we are starting on our feet our first objective is to win the takedown battle. We want to hit our opponent with the Earth as ballistically as possible. A secondary objective is to hit the takedown in such a manner as to be past my opponent’s legs. I start my guard pass with my takedown, while still on our feet.
Next I want to move towards my opponent’s back. Either cause him to give his back or find a way to take his back. This limits his offensive and defensive capabilities.
Lastly I want to lock in a choke and put him out. While getting to mount or knee on belly and raining knuckles on my opponent is a fantastic option, the most efficient way to end the fight is to choke him out. The human skull is fairly durable and can take a lot of punishment. Compare the number of strikes it takes to knock out most fighters versus how quickly even a highly skilled fighter succumbs to a properly applied choke. A choke also limits the possibility for me to damage my hands while trying to punch a hole in my opponent’s skull.
Once the choke has helped you achieve your objective, disengage from your opponent. Sit them up or turn them on their side so they can regain consciousness. Now get out of Dodge.
Not so coincidentally this strategy works regardless of whether we’re on the street or in a sport environment.