Based on my experience on the mainland, Mega is excellent. Good bakery and produce section and pleasant to shop there. Well stocked with good variety. Soriana's is nice and more up-scale then Chedraui by far, but it's also more expensive and I didn't really think it was worth it. There are lots of Mexican brands for everyday things that I'm happy with so having to pay extra for US brands was annoying with some items (again, this was in Playa, might be totally different in Cozumel since the location should get mostly locals, not renters and tourists...)
The Chedraui in Playa did make improvements as more competition came in. Every store has it's highlights and I do fine getting what I want and need at any of them. Each seems to have found their loyal following and they are coexisting well together.
Yeh, I've grown accustomed to many Mexican brands, and some I even find are superior to US brands and/or are US brands under a MX label...so that's not so much the issue with me. I have found all of the stores on the mainland to be maintained and more adequately stocked than Chedraui here. Again, I think it's because they had no REAL competition before.
Even when I make my Sam's run to the mainland, I often go into Sorianna or the Chedraui there and say to myself: "Why can't our Chedraui be this nice?" The competition here will be nice and is NEEDED