My Hero Academia was bound to derive from Dragon Ball sooner or later. Not only is the latter one of the most influential series of all time, but both manga were picked up by Weekly Shōnen Jump. That these two shonen battle manga would happen to utilize some of the same tropes and story elements should come as no surprise.
In this case, it's about how these series have handled their training arcs. Naturally, shonen protagonists undergo all sorts of training methods to get strong enough to fight bigger and badder threats. However, My Hero Academia and Dragon Ball Z happen to have training arcs that are reminiscent of one another.
The first training arc worth talking about comes from the Cell Saga of Dragon Ball Z. While training in the Hyperbolic Time Chamber, Goku and Gohan were looking for a level of power beyond Super Saiyan. However, doing this would require them to first master the Super Saiyan transformation. This wouldn't be easy as Super Saiyan, for how powerful it made them was difficult to initiate, control, and maintain.
For Goku and Gohan, the solution was simple. They would turn into Super Saiyans consistently for as long as they could. By making the transformation a regular part of their lives, it would eventually become second nature to them. By the time they completed their training, they had become so comfortable with being Super Saiyans that they could stay in the form as long as they wanted.
In MHA, Deku faced a similar issue with his One For All Quirk. Since his body wasn't strong enough to use the Quirk at 100%, any part of his body that tried would be left broken and bruised. He needed a more efficient way to use One For All that didn't involve such dreadful consequences.
During his internship with Gran Torino, he found a solution that would ensure that his body would last. He found out that he could handle exerting five percent of One For All's power without suffering any negative side effects. The next question, however, was how he could use this five percent consistently.
This is where Deku developed his Full Cowling technique. Before, he had focused on releasing One For All's power in short bursts at specific points on his body. With Full Cowling, he could apply the five percent he could use to his whole body. Since five percent wouldn't harm him, he could continuously use the Quirk without stopping.
A number of parallels can be drawn between these two training techniques. Both involve learning to handle a great amount of power and use it constantly. This is done in the hopes of someday reaching a higher level of power. Both exercises can be seen as a form of endurance training. Both forms were quickly put to use against powerful new foes; for Gohan, it was Perfect Cell; For Deku, it was the Hero Killer Stain. And, of course, both training arcs involve up-and-coming heroes who are expected to be the world's next great protector.