Riveting question on a Sunday morning, I know.
Here it's mixed. One washes under running water, one does the bowl/sink full of water thing. We both think the other is wrong- one thinks one way is wasteful, the other thinks one way is dirty (that might have more to do with the washer than the method though)- . We don't argue about it (anymore) and just let each other to get in with it.
So what happens in your household? One way? The other? Also a mix?
We don't have the space for a dishwasher, so that's not an option.