I've beaten players with Elder Azure birds with the same star level as mine (51 as of 27 July 2016). However, I'm evidently no match for players with star levels over 60, no matter the bird card levels. Virtually all high star-level players such as this one have way more gold medals than silver or bronze. They're the ones who usually wind up in fourth place or better. That said, upgrading your birds is not enough. Master Leagues, anyone? It'll give the high-ranked players something to look forward to!