My personal opinion is the BOS would slaughter the Legion army with some causalities. Lets look at there origins/ranks
http://fallout.wikia.com/wiki/Brotherhood_of_Steel_ranks
http://fallout.wikia.com/wiki/Caesar%27s_Legion_military_hierarchy
Just for the heck of it^
http://fallout.wikia.com/wiki/Caesar%27s_Legion
http://fallout.wikia.com/wiki/Mojave_Brotherhood_of_Steel#History
Now lets look at there stats:
BOS General armory:
T-51b Power Armor(helmet included)- Armor-25DT Helmet-6DT
T-45d Power Armor(helmet included)-Armor-22DT Helmet-5DT
Paladin- Gauss Rifle, Tri-Beam laser, and Gatling Laser.
Overall weapons-Gauss rifle,Tri-Beam laser, Gatling laser, Laser rifle, Laser pistol, 10mm pistol, Super sledge, and 10mm smg
Caesers Legion Armory:
Legion recruit (armor)-Armor-6DT Helmet-2DT Weapons:Throwing spears, 9mm pistol, Cowboy repeater, single shotgun, Machete, Caravan shotgun, Varmit rifle, and .357 magum revolver.
Prime Legionary (Armor)-Armor 8DT Helmet-3? Weapons:Hunting Shotgun, Machete Gladius, .44 magum(according to wiki),Power fist(according to wiki),Hunting rifle, 10mmSMG,and Marksmen Carbine(according to wiki).
Legion Veteren(armor)-Armor-10Dt Helmet-3DT Weapons:12.7 SMG, Hunting rifle, Machete,Power fist,Fire axe, Marksmen Carbine,Throwing spears,Cowboy repeater, and .44 magum revolver.
Legionary Decanus(armor)-Armor-6DT Helmet-2DT Weapons:Throwing spears, 10mmSMG, 9mmSMG, and Machete.
Legion Centurian(Most formidable foe to the BOS)(armor)-Armor-18DT Helmet-5 DT Weapons:Machete Gladius, Chainsaw, Thermic Lance, Hunting Shotgun,Marksmen Carbine,Super Sledge, and AMR.
(For the heck of it) The Legate(armor)-Armor-15DT Helmet-4DT Weapons:Blade of the East and Incendiary Grenades.
Now I did not add in the BOS initiates just in case your wondering but you may also put there stats in here as well.
NOTE: Legionary officers/Soldiers will only carry about 2 weapons at a time and will use one 1 weapon at one time...
Which do you think would win?