Yes, these conditions are still in effect in Pokemon X & Y
>A Feebas's Beauty, when raised to 170 Beauty points or more, will cause it to evolve into Milotic when it is next leveled up. This evolution method still works in Generations V and VI, although there is no way to raise Feebas's Beauty in these generations, requiring use of the Prism Scale for Feebas which do not have a maxed-out Beauty condition to evolve.
In other words, if you transfer a Feebas with a max Beauty stat transferred from generations III-IV, it will keep that beauty stat in generations V-VI, thus allowing it to evolve on leveling up in these generations. Therefore, Pokemon maintain their contest stats from generation to generation, although there is no way to raise these stats from Generation V onward.