This seems to be obvious, since you're specifying the same toothpaste and the same brushing force (and I assume the same amount of time brushing). Electric toothbrushes move much, much faster than your arm possibly could, so of course it's going to abrade more. It's like comparing hand-sanding with a piece of sandpaper and a wooden block, to sanding with a powered orbital sander (or any power sander). Of course the power tool is going to wear away a lot more wood (given the same sandpaper grit) than you can with your arm.

So when you're using an electric toothbrush, you don't need to brush as long, or as firmly. It doesn't help that many people tend to brush with way too much force anyway.