Slipping to the outside
Generally you are trying to get off the center line of the second punch of an opponents attack
or to create your own counter to the first punch, this is most often achieved by moving to the outside.
Typically the first punch thrown at you will be the jab, so by slipping outside you are not walking into their rear hand power shot (typically a cross)
Slipping to the outside then gives you the counter option of an open body, uppercuts or a new angle for straight attacks. Technically it gives you the right hook to the head as well but it’s rarely used.
If you slip to the outside of their cross, and they are orthodox then there’s some real potential for a liver shot, which could stop the fight, so you definitely want to be slipping to the outside of their cross when available
Slipping to the inside
If you are advanced technically, there are a few exceptions you can use your judgement on. If you notice your opponent tends to get squared up, then you might get the distance right to use what is almost a feint slip to the inside and then land an uppercut or a short body shot. Here are Some good examples in the video below however bear in mind the experience of the fighters used, this is Mayweather, Pac, Loma, Davis…people with incredible footwork to control the range
Use the inside slip sparingly as it’s high risk.