Question about the bypass capacitor for the cathode resistor

[AmberB]

This is probably a simple question that I should know the answer to, but I simply don't remember, and I don't have it in my notes.
Does the signal output of a triode increase or decrease when you put a bypass cap in parallel with the cathode resistor. 
The question is in reference to the difference between the old Ampeg preamp and the Fender preamp.  Fenders seem to all have the bypass cap, and the old Ampegs seem to not have the bypass cap, plus the old Ampegs have a higher value cathode resistor.

[pdf64]

Bypassing the cathode will increase gain and reduce noise, so is beneficial for input stages.
Aiken explains common cathode stage design simply and concisely, providing the equations that determine the various performance characteristics https://www.aikenamps.com/index.php/designing-common-cathode-triode-amplifiers
Plug the numbers into nickb’s online calculator to get the stage gain freq response, using the rdh4 method http://bmamps.com/CapCal.html

[Latole]

And value change tone; look at Fender blackface and Marschall

Same on output tube with cathode bias.