Everything boils down to ethnic tensions and nationalism.

First, let's wind the clocks back to the turn de siecle.

The Czechoslovakian republic until WW2 was a confederation between two, equally treated ethnic groups, Czechs and Slovakians. The Kingdom of Yugoslavia was a parliamentary monarchy - under a Serbian King, the capital Belgrade in Serbia, and was very centristic. The Serbian ethnic group came first, while the Croatian was discriminated against, which caused severe tension that sometimes escalated. ( See - Assassination of Stjepan Radić, a Croatian politician who was assassinated in the Yugoslavian Senate) Needless to say, this created a bunch of strife and ethnic tension, where Croatians felt opressed, and formed the Ustashe movement which would later lead the fascist Croatian puppet state. ( See - Assassination of King Alexander, Marseille 1934)

Let's focus on WW2. While you might draw a parallel between Tiso's Slovakian puppet state and Pavelić's Independent State of Croatia (AKA NDH) as puppets born within the context of Czechoslovakia and Yugoslavia respectfully, their MOs were different - whilst Slovakians were genocidal towards jews apropos German racial laws, NDH added Serbs to the genocidal bunch as well. On the other side, in Serbia, Mihajlović's Chetnik movement was genocidal towards ethnic Croatians. If you look at WW2's casualty reports, you'll notice the number of civilian victims compared to military victims is surprisingly high - both Ustashe and Chetniks had a habit of massacring entire villages of the opposing ethnic group, further escalating the ethnic tensions. After Yugoslavia was liberated by Josip Broz Tito's Partizans and reinstated as a Socialist Federative Republic of Yugoslavia, a doctrine of 'Bratstvo i jedinstvo' (Brotherhood and unity) was instated in order to heal and mend wounds caused by the war and political turmoils before the war. Another thing worth mentioning is that while Czechoslovakia was directly under Soviet sphere of influence, Yugoslavia, albeit socialist, wasn't, and was in a state of a cold war with the Soviet Union; which later led to the formation of the Tito-Nasser-Nehru Non-Aligned Movement.

Come 1990s, Serbian nationalists under Milošević rallied under the 1940s hegemonial-expansionist-genocidal ideas and driving on raw nationalism and all historical wounds decided to embark on a policy of ethnic cleansing and forming a Great Serbia, which after the collapse of the Yugoslavia parallel to the fall of the iron curtain, sparked into outright hostility against Croatia and escalated into a fully fledged war. Czechoslovakia simply didn't have that kind of a grudge to press, or people motivated to fight and die for the sake of nationalism.