I bought these groceries from a Lawson 100円 shop. Lawson is generally a convenience store chain, but they have some Lawson Natural beauty and health stores and Lawson 100 fresh food stores scattered around Tokyo. Most 100 yen stores are pretty similar around the city, with all sorts of inexpensive household goods, but Lawson 100 is the only one I know of that also sells fresh food.
I don't think I would have trusted groceries from a dollar store in the USA. Everything seemed bland, generic, and flimsy. Was I just being a snob? I love the 100 yen shops in Tokyo! It's possible that the goods are of similar quality and that I'm just dazzled by the novelty of items tailored to another culture. Or maybe the items really are better in Japan.
In any case, I don't remember the American dollar stores carrying fresh meats, produce and dairy from the same brands as the regular grocery stores, whereas in Tokyo, I can get many of the same brands at both the 100 yen shop and the super.
I'm going to guess that the branded packaged goods (such as dairy, snacks) are the same price or slightly discounted due to the bulk buying power of an international company, while the produce and meats are likely the better deals.
Produce in Japan is held to very high standards, to the point where I almost never find a bruised fruit or vegetable at any store (even Lawson 100), and the items are very uniform in appearance. So I imagine the produce at Lawson 100 is reduced due to variance in size or color, since it's not dented or wilted like American discount produce would often be. These potatoes are pretty small, the apples are multicolored, and the onions have some black dirt or mold on the outer skin that I'll remove and rinse before cooking. I'm getting a discount in Japan for food that, in Texas at least, would be considered normal quality.
Though really, I don't shop here for the prices as much as convenience. They are quite low, but I think most local grocery stores are reasonable price-wise. I love this place most of all because it is close-by, and I'm often running out at the last minute when I realize I forgot to buy a crucial ingredient for dinner.
To get an idea of prices, think of 1 yen as 1 penny (meaning ¥100 is around $1.00). The exchange rate isn't 1:1, but in general, that's a good guideline for thinking about food prices, considering the relative cost of other life necessities.