We've done all of our grocery shopping at Shaw's since we were married. Right after we moved to Milford, a Stop & Shop was opened right across the street from Shaw's (just under 1 mile from our house). Before the grand opening, they sent us our Stop & Shop cards in the mail. We couldn't get anywhere near Stop & Shop for several months after it was open. Once the newness of the place wore off, I started doing my banking there (at one of the supermarket branches of my bank), and since I was already there, I would by milk or bread while I was there instead of going across the street.
It took a while to find things in the cavernous store. We thought that Shaw's was big when we started shopping there, but Stop & Shop dwarfs Shaw's.
When I started comparing, I found that Stop & Shop IS actually cheaper than Shaw's on most grocery products. But the really cool thing about Stop & Shop is that they keep giving me money. They have an ongoing rewards program set up so that for every 100 points I earn, they give me a $10 gift card. Each dollar I spend is worth 1 point, and they always round up (even a penny over gets rounded to the next point). They also include the $10 from the gift card as 10 points toward your NEXT card! All of this is on top of whatever "special" rewards program they are running.
So - Stop & Shop has my bank, has better prices, and gives me money. They've got a loyal customer in me!