He was very determined. On the other hand, they were wandering and were forced to stop and take a break for a few minutes.
According to Chapter XVII of the official Alan Dean Foster novelization,
...Kylo Ren struggled to stand [on the catwalk]. As he did so, his gaze turned upward. To meet the stares of a Finn and Rey peering down at him. The shock of recognition helped him to regain his footing. Rising to his full height, he started back along the still-standing walkway, moving with determinantion. Heading upward.
Then in Chapter XVIII,
Seeking a path through the snow, shadows, and increasingly dark forest, Finn finally slowed. Where were they running to? In any event, he and Rey were out of breath...It was good, anyway, to stop.
So it seems that they were somewhat lost, had no idea were they were going, and were tired enough to be forced to take a break.
Kylo, on the other hand, was resolved to find them and was not stopping for even a moment despite his injury. Given that Rey is strong in the Force but not yet skilled enough to shield her emotions, he may have also used the Force to sense Rey's fear and track her (as @thegreatjedi suggests below).