Some similarities are they both are facing a challenge Theseus and Katniss, They also both have a chance of dying,Also they both are fighting for their people.
Some differences is Katniss has a better chance to win because she is not alone she has someone with her, Another difference is Theseus has no idea where he is because he is in a maze katniss kind of does because she been there for a while and kinda knows it.
The Hunger Games
Theseus is about to kill the minotaur
Katniss and peeta are about to win the last battle