Both are low-paying jobs with dull work. So take either offer and then go out and look for a better paying job. If you work at Kroger for a year then you can apply to work in the distribution center. That job has long hours and harsher conditions (physically) but it pays something like $13/hour to start.
For which positions? I worked at Meijer for two years as a cashier and would only recommend to avoid it if you can. I live very close to the store I used to work for and many people I worked with have left--of course, that's retail in general. I worked 3-4 days and was forced every time to stay three hours after my shift was supposed to end; they call this being "notified" as if it's a magic word that justifies this nonsense. I had a medical emergency once which started with very a bad stomach pain and told the manager I might have to go to the E.R.--her answer? It's Labor Day weekend, we're busy and sending you to the gas station as someone has called in. I stayed as long as I could before telling them I've leaving and then going to the hospital. I truly have nothing nice to say about Meijer as a former employee. I work in Kroger's pharmacy now and I'm happy here, but we're mostly left alone by store management, so that helps too.