As a kid, we always piled our washed dishes in the rinse sink and then used the tap to rinse them. Then as I got older, I saw my Mom-in-law and others fill the sink to rinse dishes in. I thought that was kind of gross reusing the water, but they told me it saved water. So, these last two years, I gave into filling the sink to rinse dishes. As I was filling up my rinse water last week, I got to thinking, this seems like an awful long time to get just a few inches of water to rinse with, seems much longer than when I was a kid and used the tap.
So, I decided to do a test. I would stack my dishes in the rinse side with the stopper in place and see how much water collected as I used the tap on each dish. I have to say, rinsing with the tap is the actual winner in the saving water contest. I barely had an inch of water collected after finishing my dishes. So I am going back to my old way that I felt was more sanitary anyway. And if you really want to be frugal. Keep the stopper in the sink and the silverware and small stuff can just be rinsed with that instead of a pass through the running tap water.
I'd encourage you to test out your size sink and see what saves you the most water.