I usually find favors to be worth around 100 flat energy. However, as with all resources, their value fluctuates according to other factors in the game. For example, Samatar Jama Barre (African Union) recently offered me 3 favors for 7 Xenomass. And, as @PhilipPittle mentioned in his comment, you can (sometimes) force AIs into war with you! YES YOU CAN, AND IT'S GLORIOUS!
I'm not sure what the parameters are, but it is possible. Elodie (Franco-Iberia) offered me a favor in exchange for a nominal amount of strategic resources. Fast forward probably 100 turns or so, Hutama declares war out of nowhere. I go to my allies (Elodie being one of them) and first try to bribe them, that doesn't work, then try discussing war. Elodie said no, BUT I had an option that said "I must insist, as payment for the goodwill I showed you earlier (-1 favor)." I obviously chose that option, to which she said, "I will mobilize my troops at once." :D
Remember the 3 favors from the Samatar Jama Barre? I went to him right after Elodie. I had a total of 4 favors with him at that point, but I didn't get the option to force him when discussing war, nor would he take a bribe of all 4 favors.
As I mentioned, I have no idea what the parameters are. I had a cooperation agreement with both Samatar Jama Barre and Elodie, but I had been holding on to Elodie's favor for much longer. Hutama was Purity, Samatar Jama Barre was Harmony, and Elodie was Supremacy.
There are simply too many factors to even guess what caused the option to appear, but the point of my answer remains: It is possible to use favors for more than simple trades.