You need to capture the "decisive moment" with regard to facial expressions and body posture in the instant that reflects both the accomplishment achieved and the toll that achievement took on the one who achieved it. To borrow another phrase, you need to preserve instants that show the "thrill of victory and the agony of defeat."
Sometimes the best "finish line" photos are composed in such a way that your main subjects are still in the final dozen yards or so before they cross the line. That's when you'll catch the agony, perseverance, exhaustion, etc. of your subjects. If you continue tracking them across the finish line, you'll then have opportunity to capture the jubilation.
A good technique to do this is to shoot from a position several yards past the finish line from a position that allows you to use a telephoto zoom lens to see the runner, cyclists, etc. as they approach and then cross the finish line. A lot of races have banners, flags, etc. that mark the finish line that can be used to frame the athletes within your frame. If you can command a position directly next to the racecourse on the left or right of the "cool down" area that allows you to have an unobstructed view of the approach, finish, and reaction so you can shoot from a lower angle, all the better. Shooting from a lower angle will make your subjects seem to tower over everything and give them a bit of an "heroic" vibe.