Warning! Spoilers for Captain America #0.
Besides Steve Rogers, both the former Captain America, and when Bucky's most tragic moment is recreated, Sam Wilson utilizes it to prove he is worthy of the mantle.
When Steve Rogers temporarily retired from Captain America, Falcon picked up the shield and took up the mantle to honor Cap's legacy. Now that Steve Rogers has returned, there are two Captain Americas in the Marvel Universe, and they both team up in order to stop Arnim Zola from destroying New York City. The Nazi scientist's plan is a classic one using a rocket. Captain America even states how much he hates rockets, referring to the World War II adventure when he lost Bucky and was dropped into the ocean and frozen for decades. When Bucky and Cap first encountered the rocket, Bucky lost his arm and was tragically set upon the path of becoming the Soviet Union's winter soldier. It was probably the lowest point in Captain America's life.
This time around, in Captain America #0 by Tochi Onyebuchi, Jackson Lanzing, Collin Kelly, and Mattia De Iulis, Sam Wilson has an unbelievable advantage in the situation given that he has wings. He's able to blow a hole in the rocket and save both him and Steve Rogers. He doesn't do it alone, though, as Sam's wings are short-circuited mid-flight. Steve then has to come in and use his shield to have a safe landing in the water. As they float in the water, exhausted from the adventure, both Steve Rogers and Sam Wilson conclude they deserve the mantle of Captain America.
The fact that both Steve and Sam work together, utilizing each of their powers shows how great a team they are. That isn't to say that Bucky and Cap weren't a great team during the war, but the situation was nearly recreated when they were battling Arnim Zola. The fact they both were able to get out of it safely working together, and both under the moniker of Captain America, shows that Sam Wilson is without a doubt deserving of the title.
Another important aspect is the fact that Bucky is no longer Captain America at all. He took up the role when Cap died. But he eventually gave it up and returned to the name of Winter soldier. Sam Wilson gave up the name Falcon to become Captain America, but now that Captain America returned, Sam Wilson hasn't returned to being Falcon. He is still called Captain America and Steve Rogers is perfectly fine with that. That alone is reason enough to show how Sam Wilson is more deserving to hold the shield and title of Captain America than the Winter Soldier.
Look for Captain America #0 available now from Marvel Comics!