Clifton has five grocery stores (at least five that I've seen, anyway): A Tesco, a Co-op, a Morrisons, an Iceland and an independent outlet called Mace. While I have shopped at all three of these stores, I primarily purchase my groceries from the Morrisons, followed by a Tesco in the Victoria Centre in the city centre, which in turn is followed by the Tesco here. The Tesco here is a small one at a fuel station whereas the one in the Victoria Centre is the size of a usual large supermarket.
While the Co-op was the first store I went to when I first visited Clifton in September 2015, I rarely go there, as the Co-op tends to have higher prices than the others (although not quite so high as Sainsbury's). I've been to Iceland twice and the Mace store once; Iceland's prices vary whereas the Mace store is located on a side street that I rarely walk down.
By contrast, in the town in Northamptonshire that we used to live in, it had three Co-ops: A large one, a medium-sized and a small. I tended to use all three on a mostly equal basis. There was a general store of sorts but I never went there.
As for my mother, she doesn't shop at any of these outlets: She receives weekly home deliveries from Tesco, which is practical for her and my brother.