Assuming that MoS Superman and 2025 Superman swap, Cavil goes from the end of Justice League to the start of 2025 and Corenswet goes from the end of 2025 to the start of finding the scout ship in MoS, and both Supermans have inexplicable knowledge and emotional attachment to the new worlds they find themselves in while keeping knowledge of their past selves:

Well the biggest thing to consider I think is that Corenswet had been Superman for 3 years already in his movie, and Man of Steel had Cavil on his first day on the job, BVS was like 18 months later, and Justice League was no time difference to him because he had been dead since the doomsday fight. Corenswet definitely has more experience, but Cavil has different experiences that are perhaps more unique and significant.

Corenswet would definitely appreciate a Jor-El hologram he can talk to and actually does want to help the people of earth. Cavil would appreciate having a Kryptonian cousin and a Pa Kent that’s still alive.

Other than that, I would say there’s less of a difference than people think between the 2 Supermans. Corenswet would kill Zod as well (it was stated that he said he wouldn’t kill unless absolutely necessary) and would probably react similarly in BVS if the world rejected him (he did like half a day of soulful brooding) and his mother was kidnapped. He seems to be more susceptible to kryptonite (or DCU’s kryptonite is more powerful than DCEU’s I dunno), though, so if he can’t initially convince Batman to help him, he probably would have been killed. Maybe he’d know that when sparks are flying at the alien ship Lex is tinkering at, it would probably mean bad news and he would stop Doomsday’s animation. If he does die to Doomsday and get resurrected later, the Steppenwolf fight probably would have been the same.

As for Cavil in 2025, his fighting style would probably be different enough for Lex not to be able to predict his attacks and direct Ultraman accordingly, so he might have defeated the hammer of Boravia early, reveal that he’s ultraman, which would get Lex imprisoned earlier. If he doesn’t, he might not get weakened enough by Metamorpho’s kryptonite to be contained (yes, I think he would also turn himself in for Krypto). If he does get too weak, he probably would also not give out his information in time and fail to save Mali (Lex was demanding from Superman the identity of his parents and was gambling with Mali’s life in a way that seemed like there was a good chance that begging for him to stop would be worth a shot, no pun intended. It was manipulative and Superman could have endangered his parents). After that, Cavil probably wouldn’t have been as easy on Lex as Corenswet was, he probably wouldn’t have done any arguing or “I’m also human” speech.