I continuously compare prices.
IMHO, Kroger tends to be more expensive even if you have their shoppers card for some items. Their generic brand items aren't very good and I've never been happy with their meat products. Coupons and the shoppers card are a must if you are shopping at Kroger.
Meijer tends to be cheaper on some items and their generic products are a lot tastier. If you are looking for speciality items or organic foods, then you are better off going to Whole Foods because they tend to be more expensive at Meijers than at the speciality store. For instance, the one brand of almond butter Meijer has sells for around $7.00 and Whole Foods sells the same brand for about $5.00 (and there are other brands as well.).
Kroger/Meijer tend to have price wars with each other - I've noticed it the most with milk prices because I'm always buying milk (it seems).
Meijer is my second choice for produce and meat. I usually go to Nino's because it may cost a little bit more, but the quality is better and tends to last a little longer than what you get at Meijer. I don't even look at Kroger's too much anymore unless I need milk and eggs or the pizza cheese and can get them cheap w/the shoppers card.
You really have to look at the flyers and it helps if you search out the coupons. If you go through the flyers for a few months and jot down notes about how much the items you use frequently cost over time, then you will get a good idea where you can get food cheaply and which stores are having price wars over different items.
Aldi's is good on price, but the family didn't care for the products there.
Also, it depends on how much you need to buy. Costco or Sam's are great options if you need to buy in bulk.
But, if it came down to Meijer or Kroger only, then I'm all for Meijer overall. I'm happier w/the overall quality of the products and don't have to worry about bad meat or going to another store because the fruit/veggies look too iffy to purchase.