This article makes sense to me.
Handwashing: the water can't get anywhere near hot enough and chances are you're using a gross contaminated sponge anyway.
Dishwashing: should be better due to high heat (impossible for handwashing unless you're using gloves. According to the article ~145 degrees is enough to at least consider the dishes sanitized). You don't need infinite amounts of scrubbing power so much as just enough to get the food bits off, which are breeding grounds for bacteria of course. Plus use of detergent helps to create an unfriendly environment even more. I'm curious about restaurants that are confident (lazy?) enough to not use detergent, though.
Absent of pure mechanical pressure, mere water, no matter how hot, isn't able to dissolve oil!