The concept of watt per hour doesn't exist / is hardly ever used. If it did, it would be a rate of acceleration. I guess one could say my solar pv production increases at 300w/h until noon and then decreases at the same rate thereafter. That would make sense.
In your example of consistent draw one could say 580Wh/h and, maths being maths, the h/h would cancel themselves out leaving 580W. Power is always indicated by watts. Energy is watt-hours.
You can't use a watt over time, the concept is undefined. You can only use a watt-hour over time.