First, a correction in the intial statement. It is not increased diameter, per se, that gives greater tension. It is increased mass for a given pitch and mensure. Because of the different types of cores, solid, rope, braided, steel, silk, gut, synthetic, etc., and how much damping material is added, strings can have varied diameters and still have the same mass, therefore the same tension, or have the same diameter as measured with a caliper, but different tensions.
Next, unlike an EB where more string mass over the magnet has greater interaction with the magnetic field and therefore more output, a DB has a dynamic top, working against itself. Up to a point, more tension on the strings, which translates to more downforce over the bridge, will drive the top more and get a little more volume and response, but only up to a point. Beyond a certain tension point, excess tension then starts damping, or "choking" the top and a player can find his/her bass actually having less acoustic output with too heavy tension of strings.
And then, depending on the construction of the strings, tension may have absolutely nothing to do with flexibility or feel, due to the nature of the outer wraps.
Sometimes it just takes some experimentation, after consultation with a good luthier or some thread research about other peoples' experiences, to try to narrow down the universe of strings and basses to a few combinations that meet the needs of the player.
Finally, to actually answer the question: it depends on all the above.