I've bene to all three. The Kash N Karry is brand spanking new, has a really good selection, and decent prices. Another thing I really liked about it was that it wasn't crowded (I've been twice in the past four weeks), and there were absolutely no lines to check out.
The produce there was really nice, although I think Publix has a larger selection.
Kash N Karry is most definitely a full grocery store. They also have a liquor store/ABC/package store (depending on where you are from) attached, so if you have those wants or needs you can get your bottles there at the same time.
My sister said the diapers were the same price as she pays back home in Litchfield County, CT (very expensive area), and I bought a couple bottles of wine for the same price as I would pay at home in a very expensive area of NJ. The produce was cheaper than home.
Publix is also nice, but the checkout lines can be really long. Albertsons is probably the most expensive of the three.
Anne