"Aldi" is actually split across two different companies that operate in different regions of the world: Aldi Nord and Aldi Süd. In the US, Aldi Süd operates the Aldi stores, whereas Aldi Nord owns Trader Joe's.
I think the problem there is that Aldi and Trader Joe's stores are in the same territory, should we be looking at localized warfare? :D . I like both, but Trader Joe's is always ridiculously crowded. They could add two more here and still be "crowded" but not "oh-my-god I can't go into that mess". I think they're leaving money laying on the table with this choice. I've lived in 3 cities and it was always the same, too much for those of us who get anxious when every time you stop to pick up something for more than two seconds, you have someone looking over your shoulder at the same thing.
For a long time there was only 1 NYC Trader Joes, in Union Square, and it was a madhouse. Fortunately they do tend to expand, it just takes a while. Off-peak hours like weekday mornings help too.