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I am wondering if Mars' body provides enough protection against radiation on Phobos. The lack of magnosphere is a significant factor highly worsening the radiation exposure, making the planet difficult to survive on for mankind. On the other hand, Phobos is protected from the Sun by Mars.
A related diagram published by NASA based on their observations The figure is from Li et al. 2016.
Phobos, on its surface, has some protection against radiation beyond being just in deep space. But the real advantage comes where Phobos is easy to dig in to, and thus you could have a habitat under the surface of the planet.
But if you compared the surface of Mars and the surface Phobos facing Mars, you would probably get roughly equal exposure. The atmosphere of Mars will absorb some radiation, but on Phobos you have the same protection from half the sky as on Mars, plus whatever area Mars is will protect you from some portion of the sky. Not sure which effect would be stronger.
