DONT WASTE YOUR TIME LEVELING UP BY BATTLES USE RARE CANDIES!!
Stats are lower.
According to
http://serebii.net/games/evs.shtml, as Pokemon battle and gain exp, they also gain EV's which are values that increase stats. EV's are gained based on what kind of Pokemon you battle, basically the Pokemon's highest base stat determines what class of EV it provides and it's evolutionary stage determines how many (Charmander gives 1 spec. att. EV while Charmeleon gives 2). All of these EV's are then added into a Pokemon's stat when it levels up (on the basis of 4 EV's = a stat increase).
Rare Candies however ignore EV's, since you're leveling without gaining exp. however the EV's are still on the Pokemon and it should receive the appropriate stat increase when it next levels up.
So there really is only a problem with using rare candies if you max out the Pokemon's level before you max out it's EV's and associated stat increases, otherwise the only downside is that your Pokemon will be relatively weak for its level (You can however increase EV associated points manually by investing a boatload of money into the protein and calcium items which raise stats with EV's, so even if you've maxed out your Pokemon's level you can still alter its stats by throwing around a large amount of money).
