[bearbin]

The same number of amps will require the same cross-sectional area of Copper, for both DC and AC.

You can use less copper for the same power with higher voltage as a reduced current is required for the same power. This is also independent of AC/DC.

[2PetitsVerres]

(nitpicking) That's correct if you take into account the skin effect when computing the cross-section area (or if you design your transmission line to avoid it. Better solution). But at 50/60 Hz, it's negligible (the "skin depth" of copper at these frequencies is around 9mm)