To me, the bigger issue among trained people is situational awareness and mindset, whether you train with self-defense focus or a "sport" focus.
I reject the idea that sport players will automatically default to upside-down chaos theory mega hyper unicorn guard the second they face a difficult self-defense situation. The guy in my avatar is pretty much a perfect example of that.
I'm not convinced that the "self-defense inspired BJJ player" has much of an advantage over their "sport" counterpart, provided the sport player has some calmness, situational awareness, and a correct mindset.
Or if there is even a non-zero difference, it's so small when compared with other obvious factors like where you live, weapons, attitude/confidence, not being a drunk dick, etc...that it's not really worth worrying about.