One way to start to think about this is the relationship between objects and abstract data types. These are both techniques for introducing data abstraction, but their approach is different and have different tradeoffs.
A detailed analysis of the trade-offs involved must be made in order to choose whether an ADT or PDA ["object"] is better suited for a problem. Some relevant questions in this choice are: How likely is it that the system will be extended? Must the security of the system be preserved, even at the expense of extensibility? Is it possible the unforeseen interactions may be desired? Is the environment dynamically extensible, and must the additions interact in complex ways with existing code? How much efficiency is required? Is it likely that there will be a large number of binary operations with complex behavior?
In general, ADTs tend towards tight coupling, yielding more predictability, performance, etc. Objects tend towards looser coupling, allowing more flexibility and extensibility. This is a reasonable microcosm of the relationship between FP and OO.
https://www.cs.utexas.edu/users/wcook/papers/OOPvsADT/CookOO... is a paper that argues them as complementary to one another. It's worth reading in its entirety, but an excerpt from the conclusion:
A detailed analysis of the trade-offs involved must be made in order to choose whether an ADT or PDA ["object"] is better suited for a problem. Some relevant questions in this choice are: How likely is it that the system will be extended? Must the security of the system be preserved, even at the expense of extensibility? Is it possible the unforeseen interactions may be desired? Is the environment dynamically extensible, and must the additions interact in complex ways with existing code? How much efficiency is required? Is it likely that there will be a large number of binary operations with complex behavior?
In general, ADTs tend towards tight coupling, yielding more predictability, performance, etc. Objects tend towards looser coupling, allowing more flexibility and extensibility. This is a reasonable microcosm of the relationship between FP and OO.