Who was the deadliest of the two well-known soldiers: a Roman Legionary or the Spartan Warrior?

Debate is good. Hopefully you guys are still friends. This question is not possible to answer, because you are talking about individuals. Individuals differ. If you are talking about two armies, this changes this a bit.

The Romans did beat the Spartans in the Republic, but this was when the Roman army was strong and the Spartan army was past its glory days. We are talking about the 200s/190s.

With that said, if I had to take a guess, I would say a Spartan army would be tougher than a Roman legion. I say this because Sparta was one of the few truly military societies. They trained all the men from infancy to fight. It was called the agoge. A life long commitment to warfare produces some great soldiers. The Romans, to be sure, were fierce as well, but they were not trained from youth.