Kindle Unlimited is launching with an impressive catalog size but not such an impressive selection.
The service costs 9.99 euros a month in Germany, slightly higher than the US price of $9.99 but about the same as the UK cost of £7.99. The KU price is also slightly higher than the cost of a Scribd subscription, which is available in Germany, but on the upside Amazon is launching with a price that is competitive with Skoobe.
Up until yesterday, Skoobe was the leading ebook subscription service in Germany. It has a catalog of 70,000 titles in German, and costs anywhere from 9.99 to 19.99 euros per month. The lower price tiers have more restrictions, including limits on how long you can stay offline. (In comparison, Amazon's service lets a user have up to 10 ebook and stay offline effectively forever.)
Skoobe is owned by Bertelsmann and von Holtzbrinck, and it has access to German language titles published by those media conglomerates. And since von Holtzbrinck owns Macmillan, Skoobe also has access to the backlist of SF publisher Tor/Forge Books.
Amazon, on the other hand, boasts that they have 30,000 exclusive titles in German. Boersenblatt also reports that Amazon is promoting the Kindle Singles available in KU as being a "fast reading experience for a short escape from everyday life".
While it looks like I was overly optimistic to expect to see Kindle Unlimited launch internationally all at once, I do think Amazon has a serious competitor in Germany. However, so long as Amazon's competitors have deals with major trade publishers that Amazon lacks, I don't think they will be able to dominate the subscription ebook market quite so completely as the dominate certain ebook markets.