While Barry Allen and Jay Garrick have gained the notoriety as the Fastest Men of their respective worlds, there has never been an actual race wherein this pair competed head-to-head... or rather... foot-to-foot, with this pair.
For Wally West, nephew of Barry's wife Iris, his speed came from another freak bolt of lightning shattering a cabinet of chemicals like has happened with Allen earlier. Adopting an alias in honor of Barry's Flash alter ego, as Kid Flash Wally eventually joined the Teen Titans before learning that his abilities were slowly killing his maturing body. Also, the origin of his abilities was suspicious given that Barry gained his from his future energized body from the Crisis on Infinite Earths.
For Johnny Quick, it was through the speed formula 3x2(9yz)4a which gave him temporary bursts of superhuman abilities. Although this was only one of several alphanumeric formulas that gave residents of his universe superpowers, photojournalist Johnny Chambers harnessed this gift into a long career both solo and alongside the All-Star Squadron. His body never deteriorated from the speed force as had Wally since it had been fully developed, and since this energy wasn't a permanent facet of his physique as with West.
Would the adult Kid Flash, after having been given a boost of immunization from Uncle Barry's lightning form, been as fast as his mentor... or even faster? Would Johnny Quick, had his super speeding momentum not lent itself towards causing him to fly at a slower pace, enabled him to perhaps beat Jay in a footrace? Perhaps we will never know.