Once new strings fully stretch out do they have less tension?
Yes. (at least is
seems that way to me.)
I have found that once you are no longer have to constantly retune every time that you go to play, not significantly more than 2 cents or so, that the strings have 'relaxed' a bit once settled to pitch, and while I have no idea how (nor the equipment) to measure the string tension, they feel less taught, have more sustain, and seem to sound better once 'relaxed' as such.
This seems to be a parallel experience on all of the many many (more than 20) different brands and set of strings that I have tried.
The only exception to this improvement observation was when I put Aquila SuperNylgut tenor strings on a baritone and tried to get up to Bb tuning, and at a certain point the tension was too much and the strings literally gave out, and at that point you can turn the tuner peg forever and the pitch never goes up, until the string thins out at a weak point and then just, almost passively 'breaks' due to how thin it is.
I did this, with these strings because there were no SuperNylgut strings for baritone. I have not looked again since, so I am not sure if they are out now.
I have NOT yet had any experience with Southcoast, nor Alohi, nor some of the other more traditional nylon sets (sold at HMS), since I really dont much like the short sustain typical of nylon strings when compared to the many other materials that are available.
Some that I have tried (that I can remember off the top of my head, I dont have my notes handy right now) are:
D'Addario Titaniums on all scales
D'Addario J71 tenor (Jake's set)
Jim Dunlop's nylon tenor set (in the green package)
GHS Hawaiian black nylon concert set
La Bella clear nylon soprano & concert
Other brands in concert & tenor scale that were black nylon (tynex)
they pretty much sound more the same compared to each other than many of the clear, black and brown fluorocarbon strings (which all have slight differences in tone and tension, which also depends upon the resonant characteristics of the specific instrument they are installed on, as well as playing technique (finger pads, fingernails, plastic or felt pick). Other materials in strings such as the Aquila Nylgut, SuperNylgut, REDS and collaborative Aquila/D'Addario Nyltech as well as the 'BioNylon' strings also seem to have a different tension from each other, as well as a different tone profile from each other, even MORESO when compared to any traditional 'monofilament' nylon strings that I have installed/played on.
Since growing out my nails on my right hand (9 months ago) I try to use them to good effect for both flamenco-inspired strumming as well as finger-picking, and the sound is significantly DIFFERENT than when I had played before without fingernails (with fleshy finger pads), and to my ear and play-feel, there is more control over the sound and volume (articualtion and dynamics), as well as an improvement in the clarity of the tone using fingernails.