While Melissa Benoist's Kara Zor-El has made a name for herself as a superpowered hero who's more than worthy of bearing the Man of Steel's famous S-shield, Tyler Hoechlin's Superman's increased presence will give her some serious competition. With their vast array of fairly similar abilities, both heroes could reasonably be called the most powerful hero in the Arrowverse. But now, we're going to take a closer look at both to see which Arrowverse hero reigns supreme.
On Krypton, Kara was a 13-year-old girl when she was sent to Earth to protect her cousin Kal-El. Immediately, it is established that Supergirl was born as a far stronger hero than her cousin. She spent more time on Krypton, with her body developing to survive on Krypton's harsher environment.
Krypton's gravity is far heavier than Earth's. Therefore, with Supergirl able to walk around and develop through that, her body is perfectly equipped to endure elements Kal-El never experienced. Growing up on Earth's gravity meant that young Clark's muscles never needed to develop to overcome Krypton's intense gravitational field. This gives Kara an edge based on the circumstances of their birth.
However, due to complex nature of space, Kara took longer to reach Earth than Kal-El, even though was kept in stasis. By the time Kara landed on Earth, her younger cousin was, paradoxically, older than her.
Because of this, Kal-El absorbed more of the sun's yellow light, thus increasing his abilities. Furthermore, by the time Kara actually started to use her powers, Superman was already a well-established hero in his own right. He had learned how to harness and utilize his abilities to fight crime.
However, the boundaries between the two thinned as Kara developed her abilities. So this begs the question: does Kara's natural talent make her Clark's superior, or has Clark Kent's time soaking in the rays extended the boundaries between them to immeasurable levels?
Arguably, the biggest factor in Superman's favor is his speed. While Supergirl is fast, Superman's speed is matched only by actual speedsters. Eobard Thawne explicitly mentions facing off against Superman in the past, and, while the results of that fight remain uncertain, it's clear that Superman was able to keep up with Thawne, even if the villain insists that he is faster than the Man of Steel.
Supergirl never demonstrates speed that really matches the sheer levels of speed Thawne demonstrates on a regular basis. While she does race the Flash in one episode, the two aren't really racing, but merely trying to punch a hole in reality. No clear winner is determined, nor are they really fighting for their lives. It's also worth noting that the Flash has reached far faster speeds than he reached during his race with Supergirl, and Thawne can move even faster than the Flash.
The two Kryptonians share most of the same weaknesses -- most obviously, a weakness to Kryptonite and red sunlight. In theory, this could hurt both of them and would pose little factor in a fight between the two.
Supergirl, however, has a key weakness in the face of Superman that the Man of Steel does not possess: her abilities are weakened due to her own anxieties and emotional state. Due to her prolonged state in a tight, tiny container traveling through space, Kara's developed crippling claustrophobia. This can cause her to emotionally shut down after a fight, should she be put in a position where she's incapable of escaping a confined space.
If Superman and Kara were ever in a true fight, this would be enough to give him a victory. However, he almost certainly wouldn't use this kind of traumatizing tactic unless he had no other choice.
Ultimately, their natural abilities only matter so much. Supergirl only really learned how to fight relatively recently. While she's improved greatly over a short period of time, her experience means little in the face of Clark's overwhelming experience in combat.
Supergirl and Superman have fought in the past. When Silver Kryptonite drove Clark into a state of madness, Supergirl managed to beat him down, but the effort in doing so pushed her to her limits. In this fight, where Clark is put into a state of instability, Supergirl technically won, even though the fight ended with both of them hitting the floor.
However, Silver Kryptonite also put Clark into a state of mind where he was blind to Kara's words and actions, making it hard to judge if Superman was at his peak abilities of perception. The Kryptonite also appeared to diminish his abilities, either due to it actually weakening him or making it impossible for him to properly utilize his strength. If he had fought Supergirl with his full senses about him, he'd probably be able to beat her.
Furthermore, Superman has demonstrated the ability to beat Krypton's greatest fighters such as General Zod. While Supergirl grew up on Krypton, Zod thrived there. Zod possesses every potential benefit Supergirl might have thanks to Krypton's gravity -- and, frankly, far more. Yet Superman won -- more than that, he killed Zod at some point.
So Who is Stronger?
Ultimately, it would appear that Superman is the stronger of the two. While they're both incredibly strong, more times than not, Superman edges out Supergirl ever so slightly.
While it's not inconceivable to think that Supergirl could best Superman in a true fight, the Man of Steel slightly outclasses his cousin. Still, these two Kryptonian heroes remain two of the strongest heroes in the Arrowverse.