Your character, whether the Lone wanderer, the Vault dweller, or the Courier, is that 'one in a million' guy or gal...the one legends are written about...
You are, for all intents and purposes a Beowulf, or a Chucullain, or a Samson...or a Hannibal...etc etc etc. The point is your physical and mental abilities are so far above those of normal men that the difference between the two is like YOU being awake, and everyone else being heavily drugged out on anti-psychotics.
Basically, you are 'the sleeper that has awakened', while everyone else is CONSUMED by the details of their horrific, mundane, daily struggle...YOU can see, and act on, the things that are above or below the threshold of other peoples consciousness...this gives you an edge in everything from decision making (with the long view in mind), to the advantage of milliseconds foresight in combat.
Furthermore, the combat-ware on your Pip-boy, even outside of vats, provides massive amounts of information instantaneously, from threat assessment (identifying the target as a raider, instead of a caravan guard, for instance) to mapping to medical treatment. Even most guys in Power armor don't have access to such sophisticated systems, since their tech is falling apart, where as yours is built to last. The pip boy is perhaps the FINEST example of pre-war tech, bar none. Like the man said 'You could drop a bomb on one and it would survive'.
Lastly, your character has that...certain something the Hannibal's and Beowulf's of the world share...that last gasp refusal to lie down and die...that extra hand grasping the threads of life that gives you the ability to keep on fighting even in the face of horrific life threatening injury...you shrug off a shotgun blast to the chest, crawl back up off the ground, and keep firing. Few people have that kind of concentration and perserverance.
Basically...you are a demigod walking among troglodytes. Enjoy the rush.
In the real world...how would an encounter with the BoS play out? You double tap one helmetless cretin in the cranium and 12 guys suddenly zoom in and circle around you and basically phaser your butt to death en-masse, with coordinated firing.
Yeah, don't put too much stock in video game AI.