Based on fossils, you have to go with the first one:
Many supporters of the multiregional hypothesis backed up their believes with the fossils found in Asia and Europe. In Eastern Asia for example they found a fossil of H. erectus of 1 million years old, a fossil of H. erectus and one of an archäic H. sapiens of 0,2 million years old and one of a modern H. sapiens of 67000 years old. So one could say you hade a gradual shift towards towards H. sapiens, which fits into the multiregional hypothesis. However, recent discoveries brought us some fossils of archaic H. sapiens of 0,35 million years old, which is a lot older than the most recent H. erectus. So supporters of the Out of Africa hypothesis say H. sapiens doesn't originate from H. erectus then, but migrated from Africa to Asia and lived on there, while H. erectus took its time to get extinct
The same story in Europe, Australia and the Middle-East, all backing up the Out of Africa hypothesis.
And then there is the genetic evidence which is also largely supporting the Out of Africa hypothesis, although there is proven to be a mixture of genes throughout the world dating back to more than a million years ago, which is in favour of the multiregional hypothesis. Pro-Africa: the fact that there's a lot more gene diversity in Africa compared to the rest of the world should prove that the modern human beings originated from that continent and then spread around the world.
Based on what I have read and learned about the origin of human beings, I'd go with the Out of Africa hypothesis.
Funny thing is: I had two different courses on the origin of humans with two different professors and they both differed in their opinion on the matter. That proves it's still not cetrain which theory is the clear cut winner