#s1P is the exact same battery as a 3S. They are diff descriptions of the same thing. Since the '1P' doesn't really mean anything, its become accepted to use the shortened version and just describe it as a 3S lipo. There obviously wouldn't be any diff in performance.

8.4v NiMh or 7 cell packs will charge to close to 12v, a good NiMh cell will charge to close to 1.5v. A fully charged 2S is only 8.4v, so the 7 cell pack will have higher voltage for a while. NiMh voltage falls off faster than lipo so after running for a while, 2S lipo will have higher voltage than the 7 cell pack will and it will stay that way until both are discharged.