For a given transmission line, if the DC current and the RMS current are the same, then the heat dissipation of the line will be the same for DC or AC.
So, this sets an upper limit on how much current the line can carry.
The voltage drop also depends on this current and the resistance of the wires.
Using a higher voltage (AC or DC) results in more total power being delivered and better efficiency.
Developing this higher voltage, and using it at the consumer end of the line, is currently easier using AC and transformers, but DC has some advantages, particularly if the transfer of power is between countries that use different electrical standards for domestic power supply.