Best rod for distance is IMHO the stiffest one you can handle, and I would bet on the tip action one, even if butt action ones can have some terrific line lifting capability. This corresponds to Paul's situation, and the extra distance is relatively small I think, but it exists and can make the difference. This does not mean that it is the case for all people, just a question of taste and "feel good" as they cast.
I interpreted this as an assumption just because it cannot exist for the full range of usable load:
MerlinSuppose, hypothetically, I have two rods with the same overall spring constant e.g. the tip deflects by the same amount for a given load, but one of these rods bends down to the corks whilst the other has the bend concentrated at the tip.