Although
@Risewild and
@mithrap mostly deconstructed and debunked various arguments presented, especially those by
@Pwener who seems to ignore them constantly, I'd just like to point out
what actual Brotherhood of Steel member is - the most average member of the Chapter - and why they are far weaker than we think them to be.
@TorontRayne made a comparison between BoS and Space Marines. This couldn't be farther from truth. (I am aware Toront said they are not the same or something in that regard, but there is a point here I'd like to make).
Without delving deep into WH40K, Space Marines are genetically modified superhumans who literally have around 20 organs more than homo sapiens, are 1-2m taller and the tech they possess
can literally destroy tanks and endure direct tank gun hits because their armor is such a tremendous feat of technology. Space Marine, even without armor, could literally tear a fully equipped BoS Paladin in two, bare handed. They are that fucking strong.
So no, Brotherhood of Steel soldiers are not Space Marines. This is extremely important point that people seem to constantly forget.
BoS are not super soldiers. Far from it.
Referring to West Coast BoS, they are inexperienced isolationist who have little actual combat experience, most of them spending lives manufacturing and dismantling technology, keeping their databases in check and spending time in VR/shooting ranges. Actual, experienced, tough-as-nails BoS members are far and few in between, because they are either too old (BoS has been in isolation for too long), under equipped (BoS has many bunkers which are locked down), have little intelligence about what's outside their bunkers to act effectively (few patrols, few fresh info) or are dead. Yes, dead, because BoS has lost many, and unlike NCR, doesn't have fresh blood to refill their ranks.
Compared to them, NCR is far, far better equipped, has much greater manpower and is (this is the part many people overlook) more experienced in combat. Much more.
NCR has thousands of regular "young blood" troops refilling their ranks, have many older, experienced soldiers that surpass BoS veterans in number, has a huge war machinery supplying their troops, have their own Power Armor units, and have elite units like Rangers which are death incarnate on the battlefield.
What do BoS have?
They have advanced weaponry which while very dangerous, is again mostly in hands of inexperienced grunts. Even then, to paraphrase Mr House, they amount to very little when you're outnumbered 15:1.
And they have the infamous
Power Armor which is not all that powerful. PA was introduced pre-War to make a sort of heavy infantry which can serve effectively in various environments (but radiation is still a bane to it, see The Glow), to offer better protection and life support to the soldier inside, but it is not an almighty piece of protection that turns people into walking tanks. PA soldiers are "walking tanks" in a sense that they can easily carry heavy, extremely destructive weaponry which regular soldiers cannot carry and which can be more effective than tanks in some environments.
But the actual soldier encased in that armor, while better protected than regular infantry, is still highly vulnerable and as exemplified with resistance to 2,500 joules of kinetic energy, they can be felled with concentrated fire of conventional weapons - which is exactly what NCR is capable of doing, and doing it damn well.
So no, BoS soldiers are no super soldiers. They are not particularly good soldiers at all. They are stagnant isolationist, most of them combat rookies compared to a huge chunk of NCR troops. Kids and old men with dangerous toys.
I get what
@Pwener tried to say with his "FO3 came before FNV", that at the time Van Buren wasn't considered canon and hence Bethesda didn't have to care about NCR-BoS war and design their BoS with such history in mind. I get it, and for the sake of the argument, let's go along with that. There are still problems.
FO2 BoS (which obviously predates any depiction in FO3) shows that they were already stagnant, too weak and of little actual importance and most likely incapable to field an expedition to East Coast. If you consider Tactics as canon, this is shown to be true, them hardly reaching Chicago. How could West BoS send another expedition to the East? They are spent.
If you don't consider Tactics canon, then you have an even weaker argument because any form of BoS you have is the isolated organization slowly fading away, oppressed by NCR who have taken huge territory and are slowly becoming a far more immediate threat and greater priority to deal with than hypothetical loot in DC ruins. This is all FO2 material.
Now, could BoS soldiers cross the wastes on foot on year long trek from one part of the US to the other?
Perhaps they could. But not in the way that FO3 showed us they did it. Not with unprotected families and children slowing them down. Not without losses. Not through every environment and against every enemy, no. Not with keeping constant radio communication with West. And they certainly would not be able to have any reinforcements from West later on - or, to be more precise, West could never provide it.
...
On a side note, I believe that there is a sort of...hmm, popular opinion, or rather, idea that power armored soldiers in SF works are nigh indestructible and extremely strong.
From the Heinlein's Starship Troopers to Warhammer 40,000, there are many works of fiction that confirm this rule and which are probably to blame for this general idea - power armored soldiers are usually elite men, specially trained, the best of the best, equipped with technological marvels which gives them an immense advantage over regular troops on the battlefield, fielding unimaginable destructive power, from lasers, anti-tank and plasma weapons to handheld nuclear launchers.
Perhaps pre-War US Power Armor troops did conform to this rule - being elite soldiers who were specially trained to use PA, with huge support to back them up.
Perhaps early-day BoS of FO1 also belonged to this category. Any other presentation of BoS does not.