Airliners.net turns out to have been wrong.

DC-8, from
http://www.boeing.com/commercial/airports/acaps/dc8sec3.pdf

has, on page 7, a diagram for DC-8-62.

With 189 passengers and baggage, 38 745 pounds, the plane is fuel volume limited at 24 275 gallons, and has a range of about 5200 nm, fitting the 5210 nm quoted by airliners.net.

But this is not the max payload. At max. payload of 51 745 pounds, the range is about 4500 nm.

Regarding Boeing 747-100, from
http://www.boeing.com/commercial/airports/acaps/7471sec3.pdf

page 3, the diagram shows the range with 385 passengers and baggage as about 4800 nm. Matching what airliners.net has to say. 189 passengers and baggage, plus 358 000 pounds OEW, should come at a bit under 400 000 pound ZFW. Also roughly 5200 nm.

Result: no extra range. A half empty 747-100 should have roughly the same range as a full DC-8-62 with the same passenger count.

Now, the diagram uses fuel burn… but there are various assumptions about reserves included.