One of the best things about the original Doom was how fast Doomguy could run: you weren't so much a "guy" as you were a "hurtling rocket of death". So it might have taken some adjustment when Quake released, considering how slow the player-movement was by comparison, though the then-novelty of true 3D no doubt compensated for it.
But now we know why Quakeguy ran so much slower: it was because the levels were smaller. That's according to John Romero, who posted a lengthy blogpost at the weekend explaining the adjustment. Basically, all Quake levels needed to be less than 1.4 megabytes in filesize, and to achieve that, the levels naturally had to be smaller than many of those found in Doom.
So how to make them feel less small? Reduce player speed, of course!
"John Carmack decided that we could get more gameplay out of the levels if he slowed down the player's running speed," Romero writes. "In DOOM the player went at crazy-fast speeds and it was incredible. In DOOM we could make huge maps and player speed was not a problem.
"With Quake's maps, the hallways, rooms, and outdoor areas were all smaller because of the file size. So slowing down the player meant it took longer to finish a level, and longer to finish the game overall."
The post also goes into some detail regarding the rather clumsy (by today's standard) level editor used to create vanilla Quake's levels. Check out the whole post over here.