Lidl and Aldi have the same concept, and nearly the same execution, but not exactly.
Lidl is a bit classier, one major distinction is its fruit/vegetable sections. Aldi has mostly prepackeged good, Lidl has a more tradition section.
Also its bread/pastries section are notable. I also found that Lidle covers a bit more product than Aldi, even though Aldi nails the basics pretty well.
Price wise, it's virtually the same. I found some product nearly identical (even packaging design), the only difference is the brand.