From a stress corrosion standpoint, lower HAZ hardness should be expected due to the lower carbon equivalenbt; however, this is not always true and, in our one size fits all world where materials are multiple stamped, buyer beware.
They are usually one and the same, being dual certified. Almost everything that meets Gr. 70 will meet Gr. 60.
There are SCC situations in refinery service where you prefer Gr 60 (or Gr 55) with a maximum tensile strength below the allowable max. in ASTM A516.
Shmulik - not automatically. Better ductility does not necessarily bring better low temperature fracture toughness.
"If you don't have time to do the job right the first time, when are you going to find time to repair it?"
brimstoner: indeed, it is not automatically. Higher elongation is required by Section II part A ; SA-516
Temperature / V-Notch energy absorption at SA-20.