Yes, that definitely makes a difference. Many of the features are only available in some countries. Generally I would say the German version offers the most features, but on the flip side you only get 3-5 free ATM withdrawals in Germany per month (some other countries have unlimited free withdrawals).
It looks like N26 is planning to start charging for the Mastercard for customers from most countries in the near future, but already existing customers will continue to have a Mastercard for free (another reason to sign up ASAP).
You can see what products are available on the pricing page (select country in the top right), and as fair as I can tell Black is now available for "rest of europe" which includes Luxembourg.