I think it's a little of both. Semirhage taunted Rand about the voices in his head being indicative of Taint madness. Truth, fucking with his head, or a little of both? Ishy's lies were often based on a grain of truth.

Conversely, Rand tells Tuon that his claim to leading the forces of LIght trumps Artur Hawkwing's because he is Lews Therin and thus predates Hawkwing by over a thousand years.

So both true to an extent? The Dragon is always the same soul but the Taint madness confuses the Dragon Reborn who can't adequately assimilate the memories of previous lives until after the Taint is cleansed? I'm speculating here, not proposing a solid theory.