Well , out of the two i would say that they both excell in different stages of the game.Ashe has a pretty good lane phase with the W and Q+Autoattacks which makes her not easy to catch up and not easy to escape from.On the other hand , Vayne is better to be put in a 2v1 Lane so he will be secured a little bit of farm that she wouldn't get because of the bullying you can give to her at the laning phase.If Vayne is playing against a normal 2v2 Bot Lane , after she hits lvl6 she is one of the strongest ADC to make a gank really painfull for the enemy as she can DESTROY enemies , and mostly supports like Sona / Janna.So , overral , Ashe has a better and safer early game and laning phase than Vayne.
Now , on the late game i think there is not much to say.Even if Vayne has a terrible score and a farm (lets say 100 creeps less than the enemy adcarry) she can still probably win the fights 1v1.But , since 1v1 doesnt matter of course and the point is to help your team to win , vayne can be itemized in so many ways and she can destroy at least 2 players in the teamfight.She doesn't even need protection to do that in lower elo.Her R+Q to lock down someone while trying to keep the best possible position to hit as much and get hit as less is just PAINFULL even for the enemy frontline.Ashe on the late game , has a GREAT GLOBAL STUN +AOE SLOW which can be game winning.I'd prefer to put Ashe with a Thresh or Lulu in the team , because they can utilize fairy well together.For sure weaker late game.
Conclusion , for me , thoose 2 ad carries are great anyway..
Thats my opinion , if you notice any mistakes let me know