[inquisitor]

@Motel75
I am aware of those past problems which where linked to the introduction of a new billing system. But they seem to be solved for a couple of weeks now and as you said mostly affected postpaid subscribers of the "Smart tariff".
Doubtlessly T-Mobile and Vodafone provide better coverage and higher bandwidth, but they charge for that accordingly. While Lidl gives you 5GB for € 15, Ja mobil and Penny mobil (the cheapest brands on T-Mobile) block VoIP and throttle customers already after 3GB. With congstar and all the discounters on the Vodafone network 3GB will cost you even € 20. Notably for the large data packs (>500MB) Vodafone discounters won't throttle your speed after exceeding the monthly allowance but they will terminate Internet access and you will have to order a new pack.
Edeka indeed offers the same international rates like Lidl but the only data option is a 500MB pack for € 10/month.
Lastly SIM cards from most providers on T-Mobile and Vodafone are more expensive, as they are all sold for € 10 but include less credit than Lidl (€ 5 vs. € 10) and do not have a customer referral program that gives you an additional bonus of € 5 for Lidl.
Depending on individual travel route and amount of data usage T-Mobile and Vodafone may be the better choice but for those who are happy with a downlink of 2-3 MBit/s and stay close to the agglomerations, Lidl is still very interesting as is cheaper and provides unrestricted Internet access.

@papeti01
Simyo is based on eplus, which is by far the worst network in Germany. If you want better coverage and higher bandwidth have a look at Ja mobil, Penny mobil which are identical and both offer 3GB for € 20/month or Bildmobil which has the following data options:
7 days for € 6.99 (terminated early if exceeding 1GB)
30 days for € 19.99 (terminated early if exceeding 3GB)
90 days for € 39.99 (terminated early if exceeding 5GB)