They occupy the same universe so we have to assume the same physics apply. Iron Man's repulsor tech is described as an inertia-less one-way kinetic blast. At higher energy levels, it can can even disintegrate matter in front of it. Cyclops’ eye beams are described exactly the same way. Is there any place in comics or the animation where the two beams are shown to have different powers?
No, Iron Man's repulsor technology and Cyclops' optically-directed ruby beam (called his optic blast) are not the same effect even though there are potential similarities in the types of damage they may both produce.
Iron Man's repulsor is a particle beam.
Iron Man repulsor technology is a particle beam weapon with explosive and concussive effects. These effects include knockback, explosions and burn effects. The repulsor has been used as a navigational aid, directing Iron Man during flight operations. The technology evidently creates more energy than it uses since Stark plans to use it and the arc reactor energy technology to generate fossil free energy.
The repulsor technology has also been used as a weapon, able to damage, concuss or destroy matter in its path. Repulsors have an electromagnetic signature and actively interact with matter in a physical process. Some descriptions describe a neutron interaction, others describe a more plasma-driven effect.
Since Stark Industries has been destroyed in the recent Iron Man Disassembled storyline, he is starting a new enterprise, Stark Resilient, which promises a business model focused on fostering international cooperation and ushering in an era of world peace. How does he arrive at this goal? Simple. By providing the world with an alternative energy source, his patented repulsor technology, Tony hopes to one eliminate Earth's dependence on fossil fuels.
Tony Stark about to try and release repulsor technology to the world as a fossil free energy source.
The mutant Cyclops' energy beam is an extra-dimensional kinetic force beam with concussive effects.
Cyclops' optic blast does not function in any way similar to repulsor technology with one exception: the optic blast can smash and compress matter in a fashion using concussion effects that resemble an explosion in terms of the type of damage dealt to the target.
The optic blast does not have a radiation signature. Nor does it emit infrared radiation or heat of any kind. It's only concession to resembling radiation as we know it, is that it travels at the speed of light and appears to be a beam of powerfully bright, red light. (referenced from a cross-over between the Fantastic Four and the Xmen).
Cyclops also has an extreme range of precision and control rarely seen with repulsors. Cyclops can spread the beam widely, blanketing an area 90 degrees in front of him. He can also tighten the beam and make it precise enough to snuff a candle without damaging anything else in the room.
The optic blast, while emitted from the eyes of Cyclops does not originate from him, nor is it "energy" in the classic sense. His eyes act as a portal to a dimension filled with the ruby "energy" and Cyclops acts as a release valve into our universe with devastating results.
The optic blast has a curious ability not possessed by repulsors. Cyclops can use the beam to carom off of various surfaces striking more than one target with the same beam. His ability is augmented with Cyclops curious sense of spatial awareness allowing him to do this using surfaces which should normally not have this potential.
Cyclops ricochets his optic blast destroying multiple targets.
That these two powers have similar effects has less to do with the source and more to do with the depiction of the effects of the damage. To the average viewer, the concussive force of a repulsor and the knockback ability of Cyclops' optic beam would seem very similar despite their completely different physical origins.