This was surprisingly hard to answer, more so since it's been at least a whole year since I last played the Jedi Consular story line ^^'
Claire is Darkside, but only because she takes the Jedi principles too far. Her complete lack of empathy makes her incredibly cold. She is willing to sacrifice innocent lives to ensure her own success. On one occasion she had to choose between saving civilians or a datacron with incredible knowledge, and she choose the datacron. People can be replaces but knowledge would have been lost forever...
So, onto her companions:
Qyzen Fess:
Claire would consider his religion and goal in life nonsense and the killing of creatures for religious points the height of foolishness. Suffice to say, they would not get along well and I doubt Qyzen would even stay with her crew.
Tharan Cedrax:
Initially she'd respect his knowledge and inventions, however, she would be incredibly annoyed by his fickleness and disgusted for the thing he has with Holiday.
Nadia Grell:
Poor Nadia would be appalled by Claire's casual cruelty towards sentient beings in order to complete her mission. Claire would not even see it as cruelty but as a simple necessity to get the job done. I imagine Nadia would be terrified of Claire and run back to her father.
Felix Iresso:
Would find Claire's way of doing uncomfortable but would grin and bear it and follow her orders. After telling her about his past she'd lose her trust in him and get rid of him :(
Zenith:
Out of all the companions Zenith and Claire would probably get along best, his willingness to murder and terrorize in the name of justice is quite alike her own black and white world view.