To break out of a grab, you must wait a variable amount of time that depends on your damage. This timer is reduced on every input of a button as well as every complete rotation of the joystick.
So, each character has both a jumping grab break and a sliding grab break. Each character has a unique animation, jumping distance, and sliding distance. Some characters, like Lucas and Wario, can get abused for their relatively long sliding break and jumping break animations, respectively.
As far as I can tell, there are only two variables that are considered to determine whether a character performs a jumping break or a sliding break.
The first variable is whether or not the character's feet are touching the ground. If the character is tall enough that his/her/its feet are indeed on the ground, that character will always break out by sliding. The exception to this is Dedede's running grab, which inexplicably causes certain characters to perform a jumping break when they would normally do a sliding break from a standing/normal grab.
The second variable is only checked if the first variable is satisfied that the character's feet are not touching the ground. If the opponent breaks out during a neutral situation (the grabber isn't pummeling at the moment), then the character will perform a jumping break. If the opponent breaks out during a pummel animation, however, he will perform a sliding break. For characters with fast pummels like Wolf and Marth, this can be very easy to control; for characters with slower pummels like Bowser and Sheik, it will be more of a luck of the draw thing, though, the grabbed player can help his chances of a jumping break by only mashing immediately after each pummel.
So, each character has both a jumping grab break and a sliding grab break. Each character has a unique animation, jumping distance, and sliding distance. Some characters, like Lucas and Wario, can get abused for their relatively long sliding break and jumping break animations, respectively.
As far as I can tell, there are only two variables that are considered to determine whether a character performs a jumping break or a sliding break.
The first variable is whether or not the character's feet are touching the ground. If the character is tall enough that his/her/its feet are indeed on the ground, that character will always break out by sliding. The exception to this is Dedede's running grab, which inexplicably causes certain characters to perform a jumping break when they would normally do a sliding break from a standing/normal grab.
The second variable is only checked if the first variable is satisfied that the character's feet are not touching the ground. If the opponent breaks out during a neutral situation (the grabber isn't pummeling at the moment), then the character will perform a jumping break. If the opponent breaks out during a pummel animation, however, he will perform a sliding break. For characters with fast pummels like Wolf and Marth, this can be very easy to control; for characters with slower pummels like Bowser and Sheik, it will be more of a luck of the draw thing, though, the grabbed player can help his chances of a jumping break by only mashing immediately after each pummel.