That "eukaryotic cells are more complex" and "compartmentalized" are used to justify the need of more level of control of gene expression. I get the basic idea but can't convince myself why complexity or compartmentalization leads to more complex control (i.e. multiple levels) of gene regulation!
In control theory, we often use multiple level of control to minimize the variance (there are few other benefits as well from design perspective); probably that is what eukaryotic cell would also do. Moreover, simple combinatorics suggest that two level of control with $n_1$ and $n_2$ molecules involved at each level respectively would give me $n_1n_2$ possibilities of output which is higher than $n_1 + n_2$ distinct output I might get if I were to use these molecules with 1 level of control/regulation.
I was wondering if such simple reasoning are correct and can be used in the context of evolution? Are there other reasons as well?