Both are equally dilute.

assumptions: when transferring a mixture of liquids, half a spoon is oil and the other half is vinegar.

Easy answer:
consider both jars to initially contain only one spoonful of respective fluid. The dilutions after the process can be easily proved to be equal in both. both jars will have half spoonfuls of oil and vinegar.

if you are not convinced
Long answer:
let both have x ml of liquids.
one spoonful:  y ml 

After first transfer, jars have  (x-y) ml of vinegar and  x ml of oil and  y ml of vinegar respectively.
After second transfer: 
 y/2 ml of vinegar and y/2 ml of oil is transferred to jar containing vinegar.

Jars now have:
(x-y/2) ml of vinegar +y/2 ml of oil     and (x-y/2) ml of oil +y/2 ml of vinegar.
Therefore, they are equally diluted.

though dilution of oil in vinegar jar is not equal to that of vinegar on oil jar.
🙂