They generally have overhead hitboxes.
They usually leave you defenseless until you land, but this particular opening goes away if you manage to land safely (strictly speaking, there is often an extremely short stun at that point, called “landing stun”). For this reason, it is more effective if the strike height is at low altitude. If a jump attack is done too high, the opponent’s hitstun will end before you land, and then you have to worry about counterattacks.
For this reason, if you hit at too low an altitude, you will be limited in that you will not be able to lead into some combos.
In 2D fighting games, cases where moves differ between vertical jumps and diagonal jumps are not few; normal moves during a vertical jump are usually geared for air-to-air combat, or have attack hitboxes aimed straight down. In the Real Bout Fatal Fury and King of Fighters series, among others, there are even differences among moves during small jumps, medium jumps, and normal jumps.
Even in 3D games, the properties may change according to the timing of rising or falling, or whether or not it is during a small jump.