Apples and oranges. The Ten Rings were not mentioned AT ALL in Iron Man 3. Only their symbol was. There no verbal reference to these guys being the ones involved in what happened with Tony in IM1, or working with Stane etc.
Not a whisper. Whereas TDKR talks heavily about it's link to the villain of Batman Begins, Ra's Al Ghul. It also talks heavily about Harvey Dent, and all the repercussions because of him and what Joker did to him, the cover up etc weigh heavily on TDKR, too.
That's why TDKR is better. It feels like a real trilogy because it takes a lot of things from both previous movies and ties them together as one complete story. It doesn't rely on Chris Nolan telling us something we should know just by watching the movie on a special feature.
But that's just it, it's not a running theme in the trilogy because nobody would have a clue they were in IM2. A theme is noticeable. In this case it's not.
Errr you can watch Batman begins and TDKR back to back with no confusion at all save for you not knowing why Bruce quit or why Rachel is dead. League of shadows has NOTHING to do with TDK... how is that any different than 10 rings in IM1 and IM3?