Gilad Bracha talks about how they're not mutually exclusive concepts, and I mostly agree (OOP can have tailcall recursion and first order functions for example). But, the philosophy seems very different: functional programming is "standing above" the data, where you have visibility at all times, and do transformations on the data. OOP is much more about encapsulation, where you "send a message" to an object, and it does its own thing. So you could totally write OOP code where you provide some core data structures that you run operations on, but in practice encapsulation encourages hiding internal data.

Though on further thought, may be this isn't FP vs OOP, because C has a similar approach of "standing above", and C is the hallmark imperative language.