I shop at a Kroger (Ralphs Fresh Fare, one of their higher-end locations) and at a Whole Foods, also about a half-mile apart from each other.
The produce is significantly better at the Ralphs. More types of produce, more produce in stock, and cheaper prices. The only reason to even go to WF for produce is for the occasional odd-ball seasonal specialty fruit that Ralphs doesn't carry.
The meat section isn't even remotely comparable. Ralphs>Whole Foods. More types of meat, more cuts, better quality, and lower prices, for both prepackaged meat and butchered meat. Ralphs even has better connections to meat suppliers if you need a custom order. The difference is so large that it would be laughable to compare the two if not for the fact that other WFs in the LA area (like Venice) actually seem to have passable meat sections.
The bar at the Ralphs is smaller, and they have no meaningful selection to speak of (4 beers, 2 types of wine), but they're dirt cheap--the cheapest you can get in the area, and easily about 1/2 the price for the same-size booze at WF.
And I've never waited 10 minutes to pay at Ralphs. What sort of bullshit is that? At the Ralphs, the manager personally apologizes to people if they have to wait more than 5 minutes in line and mans a checkout himself/herself if necessary.