Some strings definitely have lower output than others. It very much depend what material the wrapping is made of (the core is always steel, although it can be different types of steel).
Generally, from high output to low output:
-Superalloys/Alloy52
-Stainless steel
-Nickel plated steel
-Pure nickel
-Monel
I guess tapewounds are probably also in the lower end of the scale, but I very rarely use tapewounds, and only one ONE of my basses so I'm not really sure how they compare to other strings.
Flatwound strings do not have inherently lower output than roundwounds though, unless you're comparing strings that are made from different materials.
The lowest output strings I've ever played were the roundwounds that came factory installed on a cheap, entry-level Harley Benton bass. They were utterly useless (but not the same as the strings HB sell separately, which are actually quite good).
The lowest output GOOD strings I've played are Rotosound 77 flats (monel). They are lovely sounding strings, one of my personal favorites, but they have noticeably lower output than most other strings.
There are of course other factors that can affect the output too. Active basses often have significantly higher output than passive basses, and some pickups have significantly higher/lower output than others. The lowest output pickups I've ever played (except maybe the pickups in some old quirky 60s basses like Eko) are probably the Fender V-Mod P-bass pickups.
And of course, the setup (pickup height) can affect the output volume too.
Broken-in flats generally have a more mellow tone than roundwounds though, so I guess you could say they have lower output from the upper mids an upwards. But NOT a lower overall output volume.