I feel these two battling you'd need a case where they both think the others the guilty party .
- they're both after each other from 50 miles after just discovering whose guilty and believe its the other guy so they'd approach this with typical anger and psychopathic tendencies that make them the way they are from the start.
Any weapons , prep is literally the second they figure it out they get enraged n storm out like the question does is justice league unlimited for lex and how Ror does to solve the comedians death ..
So use your Imaginationfor what they may use/bring/ but I doubt they'll truly prep more than the normal hidden faces with similar dress codes lol .
Who do you think wins?