Nynaeve can now visualize the taint and the effect it has on male channelers. It presents as a black mass in the brain with various thorns that penetrate the mind. Rand, on the other hand, has a white substance on his brain that Nynaeve marvels at.

I think that the white substance is the source of Rand's power, a direct manifestation of either the One Power or the Creator's hand on Rand's mind. It allows him to heal the Pattern, ward off the Shadow and its followers, and provides him with enormous strength as a channeler.

I don't think Lews Therin ever had this power or this ability, and that the true Dragon nature was only awakened in Rand because this is a true Last Battle, unlike the last Age. Rand is now truly the Creator's avatar. He's a direct match for the Dark One, though he himself says that he's not a weapon, which probably hints at his ability to Heal the Pattern rather than challenge the dark entity.

No Forsaken is a match for him, and I'm glad I finally came to this revelation considering I once claimed in a debate with Cannoli that it was Rand vs Forsaken, and Creator vs Dark One. As an exception I would add that Moridin can match Rand. I think that Moridin will have Rand's powers, but from a Shadow PoV. We've already seen Ishamael wield enormous power in TDR when he asked the DO for aid. Rand said that it even pulled in the light of Callandor, and he got around this by cutting Ishamael off from the DO.

In summary, I'll make the following claims...

1. The white stuff on his mind is merely a manifestation of the superpower from the Creator that makes him an embodiment of the Light.

2. Lews Therin never experienced this change.

3. Moridin will have similar powers in the Last Battle and will be able to draw on enormous volumes of the TP, and do incredible things that will allow him and Rand to challenge one another.

4. Rand is a Healer, not a weapon, and that is what he refers to.