While Captain America may literally exist at the peak of human fitness, it turns out that the beer-swilling, hard-living Wolverine can outrun Steve Rogers any time he chooses, all thanks to his healing factor. In Wolverine #4 from Paul Cornell and Alan Davis, Logan goes looking for new ways to use his powers, discovering an incredible ability that allows him to run at superhuman speed at the cost of immense pain.
Logan gets this advice from Doctor Victoria von Frankenstein, the daughter of the famed Victor Frankenstein. Meeting in a secret bar used by normal humans involved in the world of superheroics, Wolverine admits that even at this point in his unnaturally long life, there are still things he can learn about his powers, and that a recent clash with a mind-controlling alien weapon has him looking for a new edge. In Doctor Frankenstein, he finds it, learning that he's always secretly been capable of inhuman speed, often using it without realizing.
Doctor Frankenstein explains to Wolverine that because of his healing factor, he has a staggering level of aerobic endurance. This is something that's long been true in his berserker rages - hugely improving his speed when he loses control - but can be harnessed to even more extreme effect. While his adamantium-coated bones cause the aerobic function of his legs to burn out quickly, his muscles rapidly heal to compensate, meaning he's capable of generating incredible speed if he can stand the pain of constantly tearing his muscles to shreds to do it. Wolverine points out that withstanding pain is one of the things he's best at, and is later able to catch up to a plane immediately before takeoff, stabbing his claws into the side so that it lifts him into the sky.
This level of speed is truly incredible, as it's likely that Wolverine is running at well over 100 MPH to catch the plane right before takeoff. Most fans would likely guess that the uber-fit Captain America could run rings around Logan, but that doesn't seem to be true. In Avengers #45 (from Jason Aaron and Luca Maresca), it's revealed that Captain America has secretly broken the world record for running a mile by one minute and fifteen seconds. While impressive, this means Steve Rogers is travelling at approximately 26 MPH (his stated speed in the MCU, according to Wakanda Files: A Technical Exploration of The Avengers and Beyond.) Even assuming Steve can double his running speed in an emergency, Wolverine still has him considerably outpaced.
Even more interestingly, it's unlikely Captain America will ever be able to match Logan. Steve Rogers' vita-ray treatment turned him into what is known in the Marvel Universe as a 'Peak Human' - a technical designation meaning that his body exists at the maximum threshold of operation for a human. While Steve must exercise to stay in shape and can have good and bad days, he specifically doesn't have room to improve - there's no part of his body which isn't already operating at peak function and efficiency. In contrast, the less athletic (though still physically impressive) Wolverine can run faster thanks to his ability to abuse his body without missing a step.
As Wolverine tells Doctor Frankenstein, exploring the limits of one's powers has long been a foundational ethos of Xavier's teachings, and his ability to run faster than any non-powered human shows why. While Captain America may be literally the fittest human on the planet, and easily one of the fastest, it turns out that Wolverine's X-Gene beats the Super-Soldier Serum when it comes to creating Marvel's athlete supreme.
