Basically from the top five most popular Euro team sports its like this (currently):
Football: CRO
Basketball: SLO
Handball: CRO
Ice hockey: SLO
Volleyball: SLO?
Hockey wise I dont think a rivarly between the two nations even exists. In fact, I think the Croatian hockey experts have always looked upon Slovenia on how to achieve maximum result with limited resources and it was not uncommon that Croatian clubs were participating in Slovenian championships and working together with Slovenian clubs on all levels (when the Croatians were interested in doing so). The two NT's have played in the same WC divisions before and there wasnt much hype about it, neither in Slovenia or in Croatia. This could probably only change if in the years ahead Croatia would put together a team that would be competitive in the Div IA and would have been able to put a fight for the two WC spots.