I think you are missing a few possibilities:

• The Serbs and Croats could each originate from a separate group.
• The Serbs and Croats could be an incomplete mixture of each other and/or other groups.

To give an example, lets ask the question who was first - Americans or Canadians? Now obviously, the question is invalid - the people in both regions originated primarily from Europeans.

Now my knowledge of this is from the fact I have a Croatian grandparent, and love genealogy, so I dug into the origins of the Croatian people. What I found wasn't that satisfying.

From what I remember, there's not a generally accepted location for where the Croatian homeland was. But they immigrated from another region, according to most historians. Genetically, Croatians seem to indicate a genetic intermixture - most plausibly, they mixed with the previous inhabitants of what is now Croatia, as well as later immigrants.

I'm not sure about the Serbs, but I believe they also immigrated from another region. I seem to recall that the migration happened at about the same time (give or take up to a few centuries).

My impression is that there's no neat origin to either group. There's linguistic and cultural similarities to each other and other groups as well, but there's genetic evidence that seems to indicate a great deal of intermixture with what is presumed to be the neolithic inhabitants of the region.