Some of it has to do with the construction and scale length of the bass, some of it's string construction, some of it's string gauge. The longer the scale length, the higher the tension will be for a given string at a given pitch. Things like headstock tiltback and top-load/string-through bridge are factors in PERCEIVED tension. They don't change the scale length, and therefore don't change the tension at a given pitch, but a lot of people (myself included) feel that the increased break angle at the nut and saddle does make the string behave a little more stiffly under the fingers and have a slightly snappier attack.
Try buying 4-string bass string sets and heavier, single B-strings (like .040"-.100" with like a .135" B) of whatever strings you already like, unless your brand offers a 5-string set like that already. Also, stainless tends to feel a little stiffer than nickel, flatwounds tend to feel a little stiffer than rounds, and hex core tends to feel stiffer than round core.
If your bass has a bridge that will both top-load and string-through, try setting it up with a disproportionately heavy B string strung through the body and lighter E-G top-loaded, and if they're hex core, all the better. Or for that matter, a hex core B with round core E-G as long as the winding composition is the same.
I personally hate them, because I personally find them hideous and difficult/distracting to play (though I'm sure I'd get used to it in short order), but multi-scale/fanned-fret basses seem to solve this problem. Depending on how radical the scale length difference is from high to low, though, they can create a new one, which is getting strings that work for them without buying single strings for each position, which is impossible from a lot of string manufacturers and expensive from any of them.