Mechanic change examples:
1) Metronome allows you to choose 10 moves to randomly choose from. Ingame, you get stupid shit like Tackle and Leer. Personally, I've been lucky with Metronome in my time using in on my Togekiss in the GF game, but I digress.
2) OHKO moves don't OHKO.
3) Many abilities were changed, like Frisk allowing you to steal your opponent's item, Anticipation granting extra evasion on super-effective and OHKO moves, and Sturdy reducing damage by 1.
4) Most status and stat boosts eventually fade after a certain amount of actions or rounds.
5) Also, speed modifiers have been changed to grant +Speed natures an accuracy boost, and -Speed natures an evasion decrease.
6) Types give added boosts, too. Ex: Grass-types gain added mobility/senses in forests, Dark-types can see in low-light situations, etc.
There are more, but if you're interested (which i highly doubt you are) check out the Data Audit here:
http://www.smogon.com/forums/showthread.php?t=85754