She actually has to choose between:
* Staying loyal to her friends and fighting in the Labyrinth with them: This is the path she ultimately chooses, even though it means putting herself in danger and potentially endangering her friends.
* Leaving the Labyrinth and joining the army of Luke/Kronos: This would have been a safer option, as she could have joined forces with the giants and potentially avoided any danger in the Labyrinth. However, she would have betrayed her friends and her loyalty to Olympus.
The choice between Janus and Hera is a misunderstanding. In the book, Annabeth gets offered a deal by Luke (who is possessed by Kronos), who promises her that he'll open the doors of the Labyrinth and help her find her father.
* Luke is associated with Janus, the Roman god of doorways, entrances, transitions, and beginnings, because he represents the opening of the Labyrinth, which acts as a portal between the mortal and the divine.
* Hera is the goddess of marriage, women, and family, representing Annabeth's loyalty to her friends and Olympus.
So, the choice Annabeth faces isn't between Janus and Hera, but between staying loyal to her friends and fighting for what's right, even if it's dangerous, and joining Luke and potentially betraying her friends for a more secure future.