The breeding advantage is obvious.
I hear a lot of people say that its useless for levelling up - but I disagree. If you level up pokemon using daycare they recieve no EVs. This makes it much easier to calculate their IVs. If you try to calculat the IVs of anewly hatched level 1 or level 5 pokemon, its usually highly inaccurate because the stats are so low. Leave it in daycare, and its stats are so high that you can make a more accurate calculation. Thus, it makes it easier to find the highest IV pokemon for breeding purposes.