I don't know how much different the languages/dialects are. I do know that from both sides people are moving towards separate languages. If we consider languages to be variations with at least a given amount of difference, they are indeed dialects of the same language. But if we consider languages to be dialects with a special formal status, they're different languages.

For an illustration of the differences between the standard Serbian and Croatian, I'd like to use an economic comparison: If I were buying a paper encyclopedia with the same content, but, say, translated into both Serbian Latin and Croatian, I'd be willing to pay probably around 50% more for the Croatian translation, simply because it's easier to use for me, it's more comfortable etc.

If the encyclopedia were in Serbian Cyrillic it would be almost worthless to me, except as a curiosity (I can read Cyrillic, albeit slower). And I was born before the downfall of Yugoslavia and have read (and own) many books in Serbian. The younger generations would probably be even more uncomfortable reading Serbian.

Elephantus (from the Croatian Wikipedia)