Eurocenticism : focusing on European culture or history to the exclusion of a wider view of the world; implicitly regarding European culture as preeminent. =]
Depends on the bullets, the "aim," the velocities, etcetera.
Assuming two exact same bullets, from same load (powder charge, primer type, from same rifle/handgun, the mass/velocities would cancel out, and the bullets would expend each other's energy and the two would fall harmlessly to the ground at the point of impact.
In reality, the same cartridges, even if fired from the same gun, would never have the bullets with the exact same velocity and weight, so the two bullets would continue in the direction of the faster bullet. More complications? the bullet type (pure lead, hard lead (alloyed to increase hardness), jacketed, and (of course) frangible bullets would all effect the outcome, but the simple answer is "conservation of mass/velocity/energy"
(I'm assuming you mean two VERY STUPID or Very Drunk people shooting at each other, in which case the "Darwin Award" should go to these two fools).
[By "bullet", I mean the projectile, as compared to the "cartridge," which would include the brass case, the primer, the powder, and the bullet]
A rhythmic disturbance that carries energy would be called a mechanical wave. A sound wave or a blast wave (or even a seismic wave) qualifies as a rhythmic disturbance. (Later with the light, okay?) Sound - or any of those other waves - involves the compression and rarefaction of air (or another fluid) or a solid, to transmit the harmonic motion. Let's look at, say, a vibrating guitar string. The string oscillates in air, and the rhythmic motion of the string as it moves back and forth creates sound. The string actually compresses the air in front of it an creates a little "mini-vacuum" behind it as it's moving forward. That space behind the string is rarefied air. The string is moving fast enough that the zillions of tiny air atoms and molecules can't instantly fill in behind that string. A blast wave from an explosion or a seismic wave works the same way. Also, there are different mediums through which the energy is going to be transferred. The medium conducts the energy. The energy is actually transferred into the medium in order to travel through it. Electromagnetic energy may not qualify to be part of this answer under the description set down in the question. The word "disturbance" suggests a medium through which the energy is propagated. Electromagnetic energy, like radio waves or light for instance, require no medium through which they must be transmitted for them to propagate. And as far as light creating "a rhythmic disturbance that carries energy" being true, think about it and come to your own conclusion. Certainly light can move through air or other media, and it interacts with the media, too (losing energy as it does). But a bit of a debate might ensue as to whether or not something like light is actually a "disturbance" as was asked. Light is moving energy - electromagnetic energy. Make no mistake about that. But if light is moving through deep space, what is the "disturbance" involved? Does it have something to do with spacetime?