War tributes depends of two great factors in normal situations (like not "Agressive AI" option on):
power rate vs theirs and war successes. If at war but no battles happened or worker/settler stolen (or undefended city captured), power rate takes full effect for war tribute. If they are more powerful (in terms of cities, soldiers, some techs, some fake power coming from diverse things like the Great Wall), you pay to make peace. If you are more powerful, they pay. If equal in power, no ones pay, but a bug happens...enforced peace treaty (10 turns peace treaty) is not accepted but a ceasefire...yes.
Now after some battles (or better said some war successes both sides), the one who gets the most is advantaged to get some tribute and it deviates the power rate influence to the winner side. For instance, in a basic situation, you worker steal early in the game. They are more powerful but accept enforced peace treaty. It is because this tiny war success change the balance to favor you.
A note about ceasefire and enforced peace treaty:
ceasefire happens if you are more powerful or/and get more war successes than the opponent or in the least simply as strong as them.
Enforced peace treaty is definitely on if you are stronger or/and get more war successes.
It means the AI cannot accept such free automatic peace without feeling losing the war in a sense. This could be a criterion for your definition of losing war.
And that would explain why the AI refuses peace treaty on equality.
War successes is a balance sheet calculated within the game based on 5 parameters:
10 points for each city captured.
1 points for each settler or worker captured.
4 points for each winning battle on the offense.
3 points for each battle won on the defense.
10 points for each nuke. I think lost units from nuke are ignored, so each nuke brings 10 and no more to avoid abuses.
A comparison is made and the one who gets more points is the winner.
War success is the criterion for capitulation system and capitulation is clearly a sign of losing a war.
Finally, there is a little parameter called ilostwar that brings one negative diplo modifier while at war; it comes if they get more war weariness than you (but possibly without happiness effect knowing AI cheats on this aspect of the game). Another aspect that can be counted as a definition of a losing AI.
@Sisiutil
You may be right about the fact it depends of the leader, but in my past tests on this subject, I tested it solely on one leader.