Well, yes and no. For some penetration mediums like mild steel, M855 is actually superior. Consider a recent research report:
They certainly behave in a similar way when they encounter tissue at the right velocities, but they aren't exactly the same.
The SS-109 can penetrate the 3.45mm standard NATO steel plate to 640 meters, while the 7.62mm ball can only penetrate it to 620 meters. The U. S. steel helmet penetration results are even more impressive as the SS-109 can penetrate it up to 1,300 meters, while the 7.62mm ball cannot penetrate it beyond 800 meters.
The current production 7.62×51mm NATO ball cartridge has remained unchanged since its adoption by NATO in 1953. As typified by the U. S. M80 ball and the Belgian M77 ball, this cartridge propels a 147-grain cupronickel-jacketed lead bullet at a muzzle velocity of 2,800 fps (848 mps). Total cartridge length and weight are 2.80 inches and 386 grains, respectively. Utilizing a standard 22-inch barrel with a rifling twist of one turn in twelve inches (M14 rifle), the maximum effective range of the 7.62×51mm ball cartridge is listed as 620 meters (682 yards). The U. S. M80 and the Belgian M77 ball projectiles can penetrate the standard NATO 3.45 mm (.14 inch) thick steel plate up to a range of 620 meters and can penetrate one side of the U. S. steel helmet up to a range of 800 meters (880 yards). In barrier and fortification penetration tests, the 147 grain ball projectile can consistently penetrate two test building blocks.
The new SS-109 cartridge propels a heavier 62-grain semi-armor piercing projectile at an initial velocity of 3,050 fps (924 mps). The improved projectile contains a 10-grain .182 caliber hardened steel penetrator that ensures penetration at longer ranges.
The new projectile can penetrate the standard NATO 3.45mm steel plate up to a range of 640 meters (704 yards) and one side of the U. S. steel helmet up to a range of 1,300 meters (1430 yards). In tests of barrier and fortification penetration however, the steel penetrator of the SS-109 could not pierce any of the test building blocks.
The primary advantages of the intermediate power 5.56×45mm NATO cartridge are summarized as follows: (1) the penetration and power of the SS-109 version are superior to the 7.62mm NATO and more than adequate for the 300-meter average combat range documented in actual battle (ORO studies): (2) the lower recoil generated by the 5.56mm cartridge allows more control during full automatic fire and therefore provides greater firepower to the individual soldier; (3) the lesser weight of the 5.56mm ammunition allows the individual soldier to carry more ammunition and other equipment; (4) the smaller size of the 5.56mm ammunition allows the use of smaller, lighter and more compact rifles and squad automatic weapons and; (5) the lethality of the 5.56mm projectile is greater than the 7.62mm projectile at normal combat ranges, due to the tendency of the lighter projectile to tumble or shatter on impact. In summary, the 5.56mm NATO provides greater firepower and effectiveness than the larger and heavier 7.62mm NATO. 5.56-mm NATO ammunition weight only 47% as much as 7.62 mm NATO ammunition.
These comparisons however, do not consider the fact that the SS-109 uses a semi-armor piercing, steel-cored projectile, while the 7.62mm ball uses a relatively soft antipersonnel, lead-cored projectile. A semi-armor piercing 7.62mm caliber projectile, using second generation technology as the SS-109, would easily outperform the smaller SS-109 projectile in penetration tests at all ranges. With respect to barrier and fortification penetration tests, the 7.62mm ball projectile can consistently penetrate two test building blocks, while the SS-109 semi-armor piercing projectile cannot penetrate a single block.
Read the entire article, 7.62 mm Versus 5.56 mm - Does NATO Really Need Two Standard Rifle Calibers? by Major Vern T. Miyagi.