Difficulty is very relative. Oftentimes you will hear people say ______ champion is easy while others will say it is extremely difficult. There is skill cap and there is skill floor. There are mobility, micro, skillshots, and game knowledge. All of these affect how difficult or easy a champion is. Let's look at each of these.
This is what I think is the number 1 factor in determining difficulty. Having mobility on your champion raises its skill cap tenfold. In a given situation, mobility can create thousands of variations in what one can do. Mastering champions with high mobility helps you choose the best ones from those thousands of variations. Champions like Ahri or Yasuo, while effective without mastery, become much scarier when there is a skilled player behind them. Yasuo in particular has a very high skill cap, because basically he has the highest mobility in the game at level 1. Skilled Yasuo's will run circles around their opponents in lane, literally and figuratively. Ahri would be one of the easiest champions in the game if her ult didn't give her mobility. However, how difficult mobility makes your champion does depend a lot on the kit. Jarvan has a dash, but because his skills are so simple and the dash is only once every 10 seconds or so, it doesn't make him very difficult.
This has to do with interesting mechanics, such as Syndra balls, Orianna ball, Draven axes, Zed shadows (this also ties into mobility), and Twisted Fate cards. Basically these force you to pay close attention to where everything is and require precision and timing. The champions above all have 9 and 10 difficulties because of this. Draven and Twisted Fate, while not hard conceptually, require tons of concentration to consistently get the desired result. It is very easy to pick the wrong card or miss an axe, especially when under pressure and when you have to pay attention to minimap, skillshots, and last hit.
Skillshots are a very generic, and even the easiest champions have skillshots. However, how difficult these skillshots are to land as well as how important they are to land affect their difficulty. If you miss your Q as Lee Sin on a gank it basically halves your damage contribution. You can miss 10 Anivia Qs in a row while hitting 10 Varus Es in a row. It all depends, but generally people seem to hold a lot of importance on player skill when it comes to landing skill shots. I think player skill does play a role in landing skill shots, but if Madlife was placed in bronze without him knowing, I'm sure he would miss a lot of hooks at first because Bronze players wouldn't try to dodge the way pros do. Basically the point is that a lot of the times it has to do with reading your opponents and how they read you.
These are champions whose skills require a good sense of the game to be used effectively. Champions like Twisted Fate and Janna can make or break a game depending on when and where they use their ults. Champions that have to commit also have this difficulty. Knowing when to go in as Kat, Leona, and Vi can mean the difference between life and death. Champions like Lux who can just throw skills out all day from the fog of war don't have to think about this.
So overall, a combination of these factors contribute to a champions difficulty. Having just one of these traits doesn't make a champion hard, but having many does. There are also champions like Ryze who have a low skill cap but have many combos to learn. How do you feel about champion difficutly? Who are the most difficult? Can we look at statistics to show how difficult a champion is? Do high win rates on difficult champions show an excess of power? Reasoning behind Riot's official difficulty rating? Does difficulty justify more power? What makes DotA and League more or less difficult than the other? Just discuss difficulty in general.
My personal top 3 are Draven, Yasuo, and Leblanc, with honorable mentions to Zed, Vayne, and Nami.