I feel like they do and they don't at the same time. The buildings may look different, but city center rents driving out a lot of small local businesses, and leaving the same brands everywhere.

You are right, that the city centers are often heavily commodified to the point where they do not differ from other cities anymore. However, European cities are not just the city center, you have a lot of different districts where the commodification has not progressed to this degree as in the city centers. Case in point, you often do have small grocery stores in those districts, mostly owned by immigrants or they are some kind of organic food store.

You're right, too, but also in the European chain stores - Carrefour and Spar, and the like - I see more quality produce and local cheese and regional products than I do in North American equivalents. They're sold right alongside the commodity, international-brand stuff, and usually is price-competitive. The best apples I ate on my last trip to Spain I bought in a motorway services; they looked like they'd been grown next door, and maybe had been.

American cities also have ethnic neighborhoods, immigrant-owned grocery stores, and organic food stores.