The source for this difference is the way how the Croats and Serbs, two related South_Slavic tribes received Christianity.

Serbs received it from Constantinople, and the the language used in liturgy was Church-Slavonic, with its alphabet based on greek alphabet.

Croatia was under influence from Rome, and even if there are early documents using glagolitic script, it disappeared and was replaced with alphabet based on Latin alphabet, as Latin was used in liturgy.

For educated persons it doesn't represent any issue. I suspect that after dissolution for Yugoslavia cyrilic script is not taught anymore in Croatia and parts of Bosnia - on other hand, there is a lot of material that is routinely printed in Latin script in Serbia, and knowledge of any western foreign language (English, French etc) requires knowledge of Latin script.