Manomay Shravage

When Supergirl was re-introduced in the mid two thousands, it was implied that she might be more powerful than superman, displaying greater speed and strength. It was later determined that her seemingly superior abilities were not due to greater power on her part, but were due to the fact that superman had spent his life on earth among humans, and was very careful not to use the full force of his powers, for Fear of permanently injuring or even killing his opponents.

Supergirl, having come to earth as a teen, had no such control over her powers. Thus, she was less concerned about the environmental impact of her speed, or the potential damage she might inflict with her strength.

The exact difference of their power levels has never been fully explained. In theory, if a kryptonian‘s strength is multiplied by the power of the sun, a person as physically large as superman would be many times stronger than the comparatively slim Supergirl (but less so than the athletically muscled Power Girl).

However, the exact way the power of kryptonians works have never been fully explained. They are simply very strong, very fast, very durable, and have very powerful laser beam eyeballs. Superman is generally portrayed as the most powerful of the three earthbound kryptonians, but, counter-intuitively, Supergirl is generally portrayed as more powerful than the more experienced and more muscular Power Girl. This has also not been explained, but it has come up several times.

So technically Supergirl would win.

Shubhanan Kulkarni

They both have the same powers, therefore, in a fight to the death, I believe Superman would win. He is older which means he has more experience fighting and you could say because of that, he is a refined version of Supergirl.

Superman would win.

Barry Rock
Older doesn't mean better or more powerful, especially since it was stated that Kara had solar panels in her ship that exposed her to yellow sun radiation for her entire journey to Earth. (And she is older than Kal, so that theory is already moot). She was augmented by her father to increase her potential for solar absorbing, and she was trained in combat on Krypton for a long time before she left. And her combat training is far superior to Earth combat skills. The absolute best Superman could hope for is that his Fortress of Solitude had training protocols of combat from his home planet that he could train with, regularly. Otherwise, Kara is older, better at absorbing/storing and using yellow sun radiation, trained in combat from 1000's of years more advanced warriors, genetically augmented with Kryptonian science and whether she learns to hold back or not doesn't actually change the fact that she is more powerful. If it is a fight to the death, every source of canon puts Supergirl as more powerful.
Aditya Kumar

Pranav Hariharane would win of course

Pranav Hari

Definitely Midoriya. The athletic tenacity and clutch decisions he makes in crunch time give him an edge in this fight.