While payload, range, and efficiency are important for tankers, militaries have reasons for still using so many 707 variants.
Many of the reasons are similar to Why does the US President fly in an obsolete 747-200? Although making an aircraft into a tanker may be less challenging than making it into a SAM aircraft, it is still a large task. The fuel system needs to be modified and significantly extended, and many other components will be upgraded to military standards. This is a large investment for what is a relatively small fleet of aircraft. It has been more economical to upgrade the aircraft rather than select newer models. Smaller fleets of tankers have been converted from existing aircraft, which is cheaper with older designs rather than the latest and greatest.
Also, like the SAM aircraft, tankers do not see nearly as much flight time as commercial aircraft. The KC-135 fleet stood at an average of 17,000 hours in 2004, with a fatigue life of about 36,000 hours. This means that gains in efficiency are less important, and other costs like maintenance and acquisition are more important.
There have only been orders for about 50 A330 MRTT aircraft. Boeing built 8 KC-767 airplanes, and there are only 3 orders for tanker conversions. The US Air Force is ordering 179 of the KC-46 tankers, with possible further export sales. This overall represents a fairly small market.
Another important requirement is service life. The KC-135 aircraft in the US Air Force have been in service for at least 50 years now. The RAF aircraft are conversions and had a long service life, but not as long as the KC-135. The 767 and A330 aircraft currently being introduced as tankers are newer designs, but still with a long and proven service history. The A350 represents a large step in aircraft design, using composites much more extensively than before. While there is certainly a good amount of confidence that these aircraft will have a long service life, militaries may want to wait until the new design concepts have proven themselves before making expensive orders.