I think that's probably arguable. Most of these kinds of definitions are much more length focused and the length does most of the same things as having a larger cartridge.
Battle rifle implies a full powered cartridge such as 7.62 NATO. Assault rifle implies an intermediate cartridge such as 5.56 NATO. Intermediate cartridges have lower energy than full powered cartridges.
Barrel length is important to velocity up to a point, but you can also tune other parts of the system to increase velocity out of shorter barrels (M855A1). However, that is far from the only consideration when discussing the ballistics of a cartridge. Projectile mass determines how stable the projectile is. The 5.56 projectile tumbles and cavitates when hitting soft tissue due to its low mass. However, that also means obstructions like foliage can cause it to destabilize in-flight and it is less effective at barrier penetration.
It's really not. Any serious discussion of "battle rifles", by military history professionals, hinges on the cartridge. I've never seen a definition of it in terms of barrel length.
Barrel length is important to velocity up to a point, but you can also tune other parts of the system to increase velocity out of shorter barrels (M855A1). However, that is far from the only consideration when discussing the ballistics of a cartridge. Projectile mass determines how stable the projectile is. The 5.56 projectile tumbles and cavitates when hitting soft tissue due to its low mass. However, that also means obstructions like foliage can cause it to destabilize in-flight and it is less effective at barrier penetration.