The difference in tension between light and medium gauge bass strings (of the same type)
is anywhere from 17% to 45%, depending on the string, the manufacturer, and the specific gauges in the set. (Non-balanced tension string sets make no sense

)
In contrast,
the difference in tension between strings of the same gauge, but different construction, is under 5% for any comparison of NPS rounds I can find. (This includes round vs. hex core and D'Addario vs. GHS, and is likely very close to, if not within, the margin of error for measurement techniques used at different times across different jigs.)
If you want to argue that a subjective difference in perceived stiffness can overwhelm a measurable 17%-45% difference in
measured tension (which most definitely affects perceived stiffness), go ahead.
I even agree with you, and I said so originally, if you're talking about the difference between rounds, half-rounds, flats, and tapes.
But my experience disagrees -- and I believe the facts back me up here --
that differences in core-to-wrap ratio and winding density can overwhelm up to a 45% measured difference. Core-to-wrap ratio affects the density of the string, which affects its tension when strung to the same note...but, as it turns out, there's not a lot of wiggle room to dramatically change the core to wrap ratio, and the end result is that most manufacturers remain in a similar range, as demonstrated by tension remaining within the margin of error. (Amongst the many reasons for this are that too much core results in a string that doesn't like to bend over the bridge or nut and produces audible inharmonicity, which is already an easily audible problem with string gauges > .100, and too little core simply breaks.)
At the end of the day, you're making a subjective argument, so it's impossible to disprove, and I'm not going to hang onto it beyond what I've already said here. But as someone who's been making my own balanced tension string sets out of singles
for over twenty years, I have a long history of experimenting with string gauges and construction, and
I stand by my statement that string gauge makes a greater difference to feel than different construction at the same gauge.
Possible exception: I have not tried the new Dogal Hellborg signature strings, which (unlike any other string I'm aware of) use
a woven central core instead of a plain steel round or hex core, and are apparently extremely flexible for their weight. They seem to be unavailable to the public as yet, but I'd like to try a set!
(It's possible to measure perceived stiffness! One would construct a jig that measures the force required to displace a string a fixed amount, at a fixed place along its length. But I'm unaware of anyone having done this.)