I want an accurate answer please. I mean it's called Morning Sun, so it should heal more, but I haven't tested this. This was introduced in Gen 2, and in Diamond/Pearl where there was a time system (morning, night and day).
>Morning Sun restores the user's current HP based on the weather conditions in the battle. Normal conditions restore ½ total HP, sunny conditions restore ⅔ total HP, and other weather conditions restore ¼ total HP.
Moonlight is also the same recovery system as Morning Day.
Hope this helps.