The 360 distance is unaffected by FOV, it doesn't mean that the sensitivity will stay the same regardless of FOV. Unless you convert using 360 distance, the sensitivity will change when you change FOV.
The conversions are related to the actual FOV, and since this is different for the two games, you get different results depending on how you convert.
This is not true, some just get confused by the fact that changing DPI from say 400 to 800 on both sides of the equation does not change the output. But the result correctly stays the same since the relation between the input and output stays the same.