Kuroko: First of all the movement is different. Player moves faster forwards than in original Quake and player moves slower when moving backwards than in original Quake.
These are my findings In a comparison between Quakespasm-Spiked and the enhanced version in the KEX Engine. On opening the Quake 1 starting hub and timing the run to the easy portal, then timing the sprint to the easy portal, both engines gave the same time. That being 3 seconds whilst sprinting, and just over 5 seconds when not sprinting. The stopwatch on my keyboard only does whole seconds, but as sprinting should be twice as fast as normal speed, this seems approximately correct, give or take some rounding of partial seconds.
When Always Run is enabled, both Quakespasm-Spiked and KEX Engine show cl_forwardspeed of 400 and cl_sidespeed of 350. They vary in their method for when Always Run is turned off, however, as Quakespasm-Spiked reduces the forward and back speed values to 200, whilst KEX Engine retains the 400 and 200 values for forward and back speed values respectively.
There is something off with KEX Engine when Always Run is turned on, though. The speed toggle to walk slows you down much more than it should. It is like it goes between sprinting and walking, rather than sprinting and running. When Always Run is turned off, though, the speed toggle does take you to sprinting speed, but when not used, the default speed is as expected, not that awful slow movement, except when going backwards. For going backwards, I have no idea why they halved the standard speed. It can easily be fixed with a console command, though, doubling the cl_backspeed value in the KEX Engine version from 200 to 400.
So in summary:
KEX Engine Always Run On
Forwards and backwards at sprinting speed (400).
With speed toggle key pressed, forwards and backwards at quarter speed.
KEX Engine Always Run Off
Forwards at half speed (running speed), backwards at quarter speed.
With speed toggle key pressed, forwards and backwards both at sprinting speed.
Quakespasm Always Run On (Vanilla)
Forwards and backwards at sprinting speed (400).
With speed toggle key pressed, forwards and backwards at half speed (running speed).
Quakespasm Always Run Off
Forwards and backwards at running speed (200).
With speed toggle key pressed, forwards and backwards both at sprinting speed.
It seems better to have Always Run turned off in the KEX Engine port, and change the cl_backspeed console variable to 400 to fix the too slow backwards speed, and this then mirrors what Quakespasm has.