HVAC distribution wins hands-down for short to medium distances, or when there are many places where you need to step up/down the voltage. It will always be cheaper to step HVAC up/down in voltage at any single point relative to DC. But HVDC transmission wins over sufficiently long distances or when crossing major bodies of water.
So I don't think we'll ever see a complete overhaul of the US distribution grid using HVDC. But we might see long-distance HVDC distribution to do things like ship solar power from the desert southwest to the west coast, or ship wind power from the Atlantic to the east coast.
The cables have water barriers so the conductors + insulation remain quite dry.
EDIT: brandmeyer's comment explains it well: https://news.ycombinator.com/item?id=16903431
In terms of km installed I think it will be HVAC just from the sheer number of offshore windfarms built over the last 10yrs in Europe. These things can be huge - 60km in length, 220kV ~1500A....
https://news.nationalgeographic.com/news/energy/2012/12/1212...