Karna and Arjuna both were the most superior warriors of their age. Let's analyze their performances throughout life
Arjuna in Drona's gurukul was regarded as the only Atiratha. He was said to be skilled in the use of all weapons. There is no such mention of Karna in Drona's gurukul except that he was a student there. Drona denied Karna the Brahmastra and Karna left to learn from Parshurama. Fast forward many years. Rangbhoomi contest. Arjuna performs great archery feats and displays his celestial weapons. Karna barges in and performs the same feats with much more dexterity, skill and ease. Karna had just outclassed Arjuna here.
But this was the turning point of Arjuna's life. He realised that there still are better warriors and archers than him and if he really wants to become the best infallible archer, he has to come out of Drona's realm. While Karna relaxed himself with all the weapons obtained from Parshurama, Arjuna started to exert himself and pleased various Gods. Being Indra's son he also gained an advantage in learning those weapons. He pleaded Agni, Varuna, Yama, Rudra, Indra, the Gandharvas and many other celestials and obtained all possible weapons from them including Varuna's noose, Yama's mace and Kubera's Antardhana. But merely gaining weapons doesn't give u an upper hand. He obtained experience by fighting aquatic and monstrous demons and vanquished them. He fought with Gandharvas and other beings to increase his arsenal of weapons and experience. Karna too, carried out Digvijaya and defeated all the kings, including the mighty Jarasandha and Bhagadatta which was an extraordinary feat. But they were mere mortals. In the Ghosha Yatra, Karna's inability to counter the Gandharva illusions of Chitrasena showed how Arjuna has started gaining the upper hand over Karna. Yes, Karna vanquished Ghatotkacha's illusionary Yatudhanas and Paulomas but they were nothing compared to Nivatakavachas and Kalkeyas. Karna was an exceptionally good warrior , but Arjuna has started increasing his level exponentially.
Karna was outclassed in the Virata war. There too, his vulnerability and Arjuna's superiority has started showcasing itself. His natural armour was taken away in exchange for an infallible dart Vasava Shakti. In the Kurukshetra war, Karna entered at the 11th day. Till then, Arjuna had acclimatized to the conditions and settled himself well. Karna started showcasing his superior prowess when on the 12th day he repelled a group attack by Arjuna, Bhima and Satyaki. But on the 13th day, he was vanquished by Abhimanyu not just once but 7 times. He did manage to cut of his bow and shield but then too, his losses were seen. His lack of concentration owing to his stopping his learning process and improvement of skills was clear. Abhimanyu was no match for Karna even at this stage. But simply being overpowered by Abhimanyu was certainly a blotch on Karna's military career. Karna lost to Bhima and Satyaki on the 14th day. He did manage to humiliate Bhima on that day, but before that he was defeated by Bhima. We can give him the benefit of doubt for fighting mildly. Whereas Arjuna had shown what destruction he was truly capable of on the 14th day when he literally crossed 3 arrays created by Drona, which included all the main Kaurava warriors, defeated them badly and achieved his goal of killing Jayadratha while Karna was rendered helpless.
A different Karna was seen from the 14th night when he started routing the Pandava and Panchala army and Lord Krishna had to send Ghatotkacha especially to stop him. Lord Krishna was clear that no one could have countered Karna in that night battle. Only he could stand in front of the Rakshasa. Karna with ease dispelled all the illusions of Ghatotkacha but was unable to kill him easily with his celestial weapons. Here again, a lack of more infallible weapons than Arjuna was seen when as a last resort he has to use the Vasava Shakti to kill Ghatotkacha.
When made Supreme Commander a more fierce Karna was seen when no one from the Pandava army could even stand in front of him. He also used his divine bow Vijaya for the first time on the day of his death. He routed everyone, repelled huge group attacks which included Arjuna, humiliated 4 Pandava brothers, used the deadly Bhargavastra and made Arjuna sweat in the last battle. He had won every heart with that performance. But his lack of patience, confidence and perseverance was seen in the last battle when he got tired and started to get overpowered by Arjuna later. He gave his best till his last breath and fought like the valiant Kshatriya he was. He was killed by the best warrior of his age after a brutal and extraordinary performance.
Arjuna excelled Karna in these skills. His concentration, experience, strategy, patience, perseverance helped him prevail over Karna. Both were extremely skilled archers but Arjuna never stopped learning even after his PhD whereas Karna remained content with graduation. This made the ultimate difference. Today, both warriors are remembered equally well and respected. But Arjuna is remembered as an ideal student. IIM Kozhikode has a statue of Arjuna to motivate its students to be a student like Arjuna.
Both gave us different lessons in life. While Karna taught never give up to circumstances, Arjuna taught to never be contented with ur progress and always aim to make ourselves better.
Considering all these points Arjuna was superior to Karna but Karna wasn't far behind.