Cracked
New member
From the image in the OP, the unicorn is a horse-like unicorn (instead of being a goat-like unicorn) and Pegasus is a winged horse of approximately the same size.
The traditional method of fighting among stallions is through biting, kicking with hind hooves, striking with front hooves, and ramming with shoulders.
The unicorn has a greater mass due to the hollow bones of Pegasus, increasing the power of the kicks and the ramming attacks.
The unicorn has an additional weapon (the horn) and can add stabbing with the horn as a weapon or can be used instead of shoulders for ramming (but that could break the unicorn's neck). However, the unicorn horn traditionally has the power to heal, so may not be effective in a fight.
Pegasus has wings as an additional weapon that can be used for buffeting.
Pegasus has flight which can be used to increase speed, and can be used in turn to increase the power of the ramming attacks.
Pegasus can also use the increased speed from flight to increase the power of kicking with hind hooves, while staying out of reach of every attack from the unicorn except for the horn.
The pegasus would win according to your fine analysis here. However, I am going willing to look past the physical and into the supernatural mythology of these two horse-like beings. If we do that, we might give the unicorn the advantage because it is, perhaps, capable of some sort of magical ability--while the pegasus is traditionally seen as a flying horse only (more or less).
So, in short, one rainbow laser beam from the horn of the uni, and down goes horsefeathers...