On a headed bass, there is a greater length between the two absolute fixed ends, the bridge/tailpiece and the tuner, as there's a non-sounding length of string between nut and tuner.
Assuming two identical strings, the tension on the string for the same scale length and same note will be the same, so headed and headless will be the same tension.
In order to fret a string, you have to push it down, which deflects it very slightly so it needs to stretch by a minute amount. That minute amount will be less of a proportion of the length between the fixed ends for a headed bass than a headless. I don't think you'll feel the difference in the real world unless your action is a couple of cm at the 12th fret.