As far as I know, there's an idiom 'David vs Goliath', so what is the opposite called? Say, how do I describe a war between two equally strong players?
You can say that the warring factions are 'evenly matched'
Evenly - adverb
3- With equal amounts for each person or in each place evenly distributed/divided
Incidence of the disease is fairly evenly spread across Europe.
The two teams are very evenly matched (= are equally likely to win).
You could describe the two parties as worthy opponents (for eachother). Or describe their conflict as a fair match-up (or any other valid synonym that applies in your case).
A Mirror match could be used to describe a fight between two people with almost identical ability.
From the sources I've found it comes from computer games, playing the same character against each other, but I'm sure it is used in real world situations as well to describe this scenario
I would use Parity personally. It's often used for both matters of money and war.
"A problem that has troubled the U.S.-Soviet relationship from the beginning has been the issue of parity" (Charles William Maynes).