Aldi does offer a Specially Selected Super Premium Vanilla Ice Cream that contains just five ingredients: cream, skim milk, sugar, egg yolks, and vanilla extract. It costs a bit more than the Sundae Shoppe and Belmont brands. Aldi Reviewer reports that it's regularly priced at $4.19, as opposed to $2.89 for the cheaper product. However, this is still lower than the regular price on a comparable product from Breyers (though you're more likely to find the latter on sale or with a cents-off coupon).

Still, the reviewer did a spoon-to-spoon comparison of Aldi's Super Premium Vanilla with Breyers' Natural Vanilla, and found that the former item came up short in several categories. While Aldi's ice cream scored points for being a bit more "natural" due to the fact that Breyers ice cream contains an additive called tara gum, it also contained about double the amount of calories, fat, sugar, and sodium. In terms of how the taste and texture compares, the reviewer admitted that three out of four family members preferred Breyers in a blind test, finding it to be smoother and creamier. 

While this review was overall inclined to favor Aldi's ice cream simply due to its lack of any artificial ingredients, such a preference pretty much hinges on the label revealing the whole truth. As the lawsuit over Aldi's other vanilla ice cream indicates, this may not always be the case — so it's a good idea to check over those ingredient lists.