A fully charged battery is a fully charged battery. Personally I think it makes more of a difference to charge it slowly (via USB) then to charge it quickly (2amp tablet charger) but I don't have any facts to back that up, just opinion.
The only thing that makes charging "off" better, is that it's faster. When the phone is on, some of the charging current it kinda wasted as it goes to the battery, but then the battery is being used because the device is on. If the device is off, the full current goes directly to the battery with nothing else drawing that charge away from the battery.