I shop at Aldi a lot, and they have some great generic brands. There ice cream is really good, and there pizza is too! I think that to much importance is placed on name brands because if you ever look at the ingredients, the generic has the same ingredients as the name brand. I like name brand for certain things, like my butter, but other than that, I buy a lot of generic brands because they are just as good if not better.
I seldom buy ice cream, but if I do, I mainly choose one brand over another due to the type of flavor I want. For example, we recently bought the flavors that were part of the competition on Celebrity Apprentice to see which one we liked best.
If you want value and a gourmet taste, try the "Fresh and Easy" store brand Ice cream. They have an incredible Vanilla Bean ice cream, a Black Cherry chunk and so many more. I bought it as a bonus points item (you pick out electronic "coupons" in their Friends of Fresh and Easy Club which add up to cash on future purchases) and could not believe the flavor and quality. If you read the ingredients you would think you are buying a high line like at Whole foods and they are so much less than the national brands. I will never pay more for Ice Cream again and even the ice cream "snobs" I know thought it was fantastic.
I love the Breyers brand of ice cream that they sell at Stop & Shop. I especially love the Vanilla Bean Breyers ice cream that they sell. I have tried the Stop & Shop brand of vanilla ice cream a couple times and I didn't really like it as much as I like the Breyers brand. I don't really know why I didn't like it, all I know is that is wasn't as good as the Breyers brand which is what I usually buy.