Buff a champion by exaggerating their strengths, nerf a champ by exaggerating their weaknesses
To the armchair game designers who make posts on this forum every day:
When opportunity allows to change a champions mechanics (because there is still room to work with without getting silly), this is the ideal balancing method because it reenforces and strengthens a champions fantasy and gameplay identity.
If you nerf a champion by toning down their strengths or buff a champion by taking away some of their weaknesses, you run the risk of watering down the champion pool into a bunch of similar kits where only the one that has the most stats at the moment is relevant in the meta. That is to say, when you're making a non numeric, mechanical change to a champion this is what you need to keep in mind.
Of course if a champion is like teemo or riven and already has a unique kit and identity, you need to be a little more subtle in your adjustments so things don't get out of hand on way or the other. If you want to exaggerate riven's defensive weakness without her shield any more, you'd almost have to give enemies a damage amp on her, meanwhile if you wanted to strengthen her identity with a buff you need to consider that most people who play riven do so constantly and will squeeze every last drop effectiveness out of any buff so you have to be super careful. Teemo is already satan to melee champions so you don't want to excessively strengthen that part anymore, and he already gets deleted by burst mages... so in these kinds of cases you probably want to stick to minor number tweaks.
But in cases where mechanical adjustments beyond numbers are on the table, that's when you need to keep in mind buffing the strengths and nerfing the weaknesses.
That means - don't touch iconic mechanics of a champions kit unless it's to improve it in some way, if you're trying to pull some power back to make room to buff other parts then pull the power out of places that are already weak. If you want to nerf nasus, removing his stacking is out of the question - even if you buff other places - since it would ruin his identity. Don't remove vayne's three hit silver bolt tank shredding (you can mess with the numbers and types of damage, just not the tank shredding aspect), don't remove teemo's mushrooms, don't let some abilities arbitrarily kill trynd or kayle through their ults, don't take away ahris triple dash ultimate, don't make new fiora riposte block some things and not others, don't take away fizz/vlad/elise untargetability spells, don't take away garen's spin2win, etc. you get the idea.
TLDR: Iconic mechanics of a champion aren't on the table for balancing nerfs. You can touch the numbers, but if you find yourself typing out a rant about why x champion shouldn't have y thing that is a core part of their fantasy or playstyle (like teemo's shrooms) then takea deep breath and don't bother posting because you're wasting everyones time. Core champion mechanics are good places to buff to strength the identity (think when they made singed flip able to snare when tossing into his glue), but they are terrible places to make mechanical changes just to bring the win % down a notch or two.