Neo, as The One, is the return of The First... the "man born inside" and shares the same powers, abilities, and eventual destiny. However, interpretation needs to be careful and critical.

Argument

"¹ When the Matrix was first built, there was a man born inside who had the ability to change whatever he wanted, to remake the Matrix as he saw fit. ² It was he who freed the first of us, taught us the truth. As long as the Matrix exists the human race will never be free. ³ After he died the Oracle prophesied his return and that his coming would hail the destruction of the Matrix and the war, bring freedom to our people."

Most recognize that Neo is a return of The First, but we need to analyze what are their similarities and differences. We are given little to work with so critical and logical literary analysis is necessary. Of everything above that Morpheous says, the second line and The First's death does not apply to Neo directly. Those events are past tense and moreover have not been duplicated- yet- by Neo. Again we work with what we have not future possibilies. And even so, such accomplishments would have to be in the macro or figurative sense because strictly speaking, Neo was taught the truth and not the other way around (unless you go macro).

What applies are the statements about The First's abilities and of The One's destiny. We should approach both from a figurative sense and interpret accordingly. The abilities are discussed here and the nature of the Matrix here. But essentially our interpretation is that The First had abilities equal to Neo's which were not god-like and the destruction of the Matrix as a means of enslavement (not eliminated in the absolute sense). If it ceases to exist as a means of control, the statements can still be figuratively true.