Disclaimer I have spent most of my youth in a variety of martial arts, and the last 10 years focusing on bjj/judo/boxing. However I have experience in aikido, Japanese jiujitsu, TKD, hopkido, and a few styles of kung fu that I've sat in on.
My take on bjj/judo or any other sport art is that it should always be the go to art for someone who wants to learn self defense. This has nothing to do with the tactics or techniques taught, but rather the training methods employed.
First, most grappling arts start you with what I call worst case senario training. Because you are new you are man handled and dominated in your training. You are learning the most important parts of bjj the first month. That is how to get a better trained, stronger, faster, younger, etc person off of you with solid physics and efficient body movements. Without these things, even the 'dirty' techniques like eye gouging could just piss off the same guy with better positional advantage who then takes you from a beating to a maiming.
Second, contact sports in general teach (and especially combat sports) you to to deal with the realities of pressure. How do you react when your punched in the face? Can you keep your clam while you have 250+ pounds on your chest? Do you panic when that choke sets in? How is your breathing in a general fist fight? While real combat is much much more intense, this is still one of the most valuable skills you can develop.
Third, sport training brings out good muscle memory habits. Though boxing I have been trained to punch the moment I get punched. You hit me, I hit you, and I keep moving. I don't think about this, it doesn't matter how much pressure is applied, this always happens (I even punch while falling from a flash KO), bjj has taught my body to never be flat on my back and to keep moving no matter how tired I might be. I don't have to think about my weight distribution, it just happens though years of learning to hold down stronger, larger opponents. Finally Judo has taught me how to fight for grips subconsciously and to always put my opponents off balance. I don't even think about this either, while I grab I'm just working to put you off balance. It's so ingrained that my wife gets mad when she goes to hug me and I pummel under-hooks or pull her to take her balance.
Forth, you gain insight into people's body types and abilities. After being around real athletes in these sports (most much better than I am) I can tell what a good grappler looks like, or a good boxer. I can see how they move in everyday activities and I know when someone is truly dangerous.
Fifth, you get humble and fast. Most non-sport guys I have met in my life are not humble. They (not even including if their art works or not) tend to be so sure of their deadly abilities is pretty scary. Anyone who spends time in a sport knows what it is like to lose. They know what it is like to be dominated and to be powerless. They understand that even when you are better trained and better equipped, you can and will still lose.
Now with all that said, the tactics of many combat sports are probably not the best tactics for self defense. Yes taking a guy to the ground is probably a bad idea if he has friends. However, the idea of worst case first means the bjj guy is better equipped to stay alive and get up if he ends up on the ground. The boxer is better equipped to land that eye gouge, and the thai boxer can probably land that crippling knee to the groin or kick to the knee much better than the non sport guy can.
So I tell new guys to start with the sport arts. They will give them the fastest gains and prove very useful as a basis for evaluating the non sport arts and fighting strategies later. AKA it's those base skills you learn in sport that make those advanced and dirty fighting strategies work. Fundamentals are always fundamental.