In 1992's Doomsday became the only villain to defeat and kill the original Man of Steel. However, Clark Kent's son, Jon Kent, has proven to be a more competitive contender since his introduction in 2015. The new Superman's human DNA combined with Kryptonian could actually make him a better match against Doomsday.
Batman's research demonstrates that Jon Kent's powers can succeed his father's. The young hero has a high level of solar radiation absorption, invulnerability, and rapidly growing strength, which could make him more powerful than his father. His and Doomsday's capabilities, too, are parallel in several ways. Both of them have Kryptonian in their systems, exhibit incredible superhuman speed and strength, and began fighting battles very young. Doomsday and Jon Kent are at the top of their fighting games, so a match between them would ultimately come down to finding each others' weaknesses.
One quality of Doomsday that gives him a leg up is his immortality. Although Doomsday's official origins are still in question, the villain's birth on the dark and violent planet, Krypton, made him indestructible in the long run as only the strongest could survive this environment. However, his intense nature outlasts anyone who comes into battle with him, and he takes advantage of his opponents' weaknesses. On the other hand, Jon Kent is susceptible to Kryptonian radiation and heavily relies on solar energy to give him the strength he needs for battle. If Doomsday sees Jon lacking energy and hitting rock bottom, the villain won't hesitate to exploit that weakness.
Even though Doomsday's immortality could make him a potential winner, Jon Kent's Superman cannot be discounted. His half-Kryptonian half-human DNA can be advantageous. His speed, strength, heat vision, and flight sur his father's, and his invulnerability grants him accelerated healing, where he can rapidly cure any wound he suffers. One of Doomsday's weaknesses is being single-minded, and he is used to quickly coming out on top. Seeing Kent heal so quickly could throw him off his game. Although it could be a stretch as Doomsday is strong-willed, Kent's moral com could create a different battle for the villain. Much like his father, Jon's desire to help others means that he'll put every ounce of effort he has into the fight as long as it means saving lives.
The battle of Doomsday versus Jon Kent would depend on who relies on and executes their strengths more. Although Doomsday has an advantage through immortality and has defeated The Man of Steel once before, Jon Kent's Superman can potentially put up an even more powerful fight against the villain.
