I used their great HA to defeat the Hungarians and, like you, took Ragusa and Zagreb.

But I had a healthy alliance with the Turks so I decided to move forward into Italy, while I established Vienna/Budapest/Iasi as Northern border. When I was halfway through Italy the Turks betrayed me, but they could not stand long against Egypt and Byzanz, especially as they betrayed me although they had big problems against Egypt alone
I found fighting Hungary much more difficult than fighting the Turks, but that can just be a time problem (war against Hungary was much earlier than the war against the Turks).

I don't know (yet) how they perform versus the Mongols or Timurids. The Mongols should be easy, but the Timurids might be a tough enemy.