Rand may very well discover aspects of the Power never conceived by LTT and his AoL ilk, however, I doubt he will necessarily "surpass" him insofar as sheer knowledge. However, this is an irrelevant point, as the two are fusing together, therefore sharing that knowledge, memories, emotions, etc.

However, I think that the important lesson Rand must learn is that the key to his success will not lie in the One Power. That was Lews Therin's mistake, and, point in fact, it was the Aes Sedai's original mistake that got them in this whole mess in the first place. Using the One Power, they sought a higher power which lead them to the DO's prison, making the Bore. LTT gathered the Hundred Companions together in an effort to reseal the Bore, with famously awful results.

Now we come to Rand... He's down one hand, has spotty vision, gets sick whenever he embraces Saidin... If his probability of winning is reliant on his ability/skill with the One Power, everyone should be running to the Ogier to open the Book of Translation.

If you ask me, his ability and strength in the One Power are significant, but not the source of his true power. Remember, he is Ta'veren. He's linked to the DO's champion. He has the breadth of Lews Therin's life meshed with his own upbringing. These are all going to play integral roles in what he does to save the world from annihilation.