This is inspired by the academy thread but it focuses on moves and abilities.
Exactly as the title says.
Do you directly port over stats and stat changes? Do you throw out the system completely? Or do you modify the game system?
I prefer to throw out the game system and cobble together my own. Simply because the game system is too simplistic and just plain doesn't work in a real-time, freeform battle that I tend to write my pokèmon battles as.
I'm still formalizing it but here's what I have so far:
I disregard numerical stats but I do hint that some pokèmon might be stronger or faster than others due to a genetic basis. EVs are ignored completely.
Also of note is that evasion boosting moves are treated more like a flashbang — something to confuse your opponents with.
Morever, projectile attacks essentially ignore typing.
Attacks can be combined to devastating or not effect.
Competitors can also use "environmental attacks" such as throwing sand at your opponent, collapsing part of the arena on them, etc.
Held items can be forcibly removed and used against the bearer — even if the attacker doesn't know Thief or Fling.
Fling is treated as an inherent "ability".
Every attack can be used in an offensive manner.
Some moves are specifically banned from competition because they are simply too dangerous. An example from one of my fics was "Aqua Laser" – a Water Gun attack that acted more like a blade of water.