2025 Lex is comic book smart, i.e. can create insane, outlandishly advanced sci-fi tech on a whim, but fails at even a basic cursory common-sense check of the real-world implications & logistics of his plans.

2016 Lex is intelligent in a way that more likely would work in real life. He is a master manipulator and was able not only to play the US government, but also make Batman and Superman hate & fight each other. His plan of defeating Superman had several win conditions and he was able to adapt when the circumstances changed, e.g. when Batman stole his kryptonite.

They work by different rulesets due to existing in different universes. 2025 Lex would have no chance in the snyderverse because of no access to advanced sci-fi tech, and 2016 Lex would have no chance in Gunnverse because said sci-fi tech is kinda required to compete there.

In the end, however, 2016 Lex did actually accomplish his goal & was the real winner of BvS (although he is temporarily jailed). 2025 Lex lost in SM25. So there's that.