I've tried Ezreal (he's actually really fun, and his mobility isn't that hard to punish, so he's fun to play against), but I can try to help out.
The adc's I play include Caitlyn, Jinx, Sivir, Ashe (although rarely), Miss Fortune on occasion, and Vayne.
Jinx: long range poking, close range dps, no mobility out of passive, moderately easy to dodge cc, long range execute
Ezreal: poke and auto weaving for max dps, AS steroids and spell on-hit effects, multi-target ult, moderate mobility
Here's the thing about Vayne. Her Q doesn't make her super mobile, the best it can be used for is to juke. Which you should do. A lot.
In laning, you use her Q to dodge skillshots and then use your next boosted aa on the enemy champion to get some good poke in. Don't max her W first, max your Q. A lot of players, including me, take three ranks in W (to make it easier to last-hit and for reliable damage) then max Q for the 2 second cooldown. Use your trinket on the bush if the support hides there (Blitz says hello!) and condemn them for the stun. If you have a support like Leona or Annie and pull this off... well, you should be able to deal a respectable amount of damage. Don't be afraid to use condemn as a reverse gap closer (lol) if you need to run.
As Vayne, you need to play with your support early game. If you get the upperhand, be aggressive, but know how to play safe. You can't hop walls like Ezreal, or expect to run away or cc the enemy with Jinx. Vayne is a late-game monster. You can wait ten-fifteen minutes before you start making the enemy your bitch. Farm, get that cs. Try to last-hit as much as possible. Know how to farm under tower (you WILL be pushed if they have waveclear).
Teamfighting, don't be afraid to focus the tank. Make the tank your bitch. Make them fear you. If the enemy team doesn't have a tank, they can't soak up damage, and everyone on your team can do their job even better. You don't have to 1v5 or kill the squishies (but try killing them if possible). You are the tank killer, that is your main target. The assassin or mages focus the squishies better than you with your short aa. Focus the tank, make the enemy team vulnerable.
One trick for escaping is ulting while in a bush, then tumbling to another bush to confuse your enemy. Then GTFO in the opposite direction they go (doesn't work if they warded, so it's very risky!).
