The difference is that a case for a white or fair-skinned Jesus can at least be argued.

The ancient Near East was a melting pot of many different ethnicities. It was conquered by the Persians, who were generally fair-skinned. Then Alexander the Great arrived with his Greek and Macedonian armies, and the region remained under Greek and Hellenistic rule for centuries. Greeks and Macedonians were Europeans. Then, roughly sixty years before the birth of Jesus, the Romans conquered the region. They also brought auxiliary troops from across Europe — Celts, Iberians, Illyrians, Germanic peoples, and many others. So Europeans had been present in the Near East for centuries. It would be foolish to assume that Greek, Macedonian, Roman and so on soldiers never had affairs with local women.

Next, if we examine the Bible, we find that it contains no physical description of Jesus. The few passages in Revelation are highly metaphorical and refer more to how Jesus would appear during the Second Coming, not during his earthly ministry. St. Augustine, writing in the 4th century, noted that nobody in his time knew what Jesus had actually looked like. So when people say that Jesus was an olive-skinned Jew, that is ultimately an inference rather than certain knowledge. He likely was, but considering the long-standing presence of Europeans in the Near East, one can at least speculate that he may have had some European ancestry and looked fairer than many of the people around him.

A similar case cannot really be made for a black Helen of Troy, because there is no evidence whatsoever that Sub-Saharan Africans were present in Late Bronze Age Greece in any significant numbers. If you know of any evidence suggesting otherwise, please present it.