oo style is great at extending types. You can add a subtype at a later date without modifying existing code and it just works.
Functional style is great at extending behavior. You can take an existing type and implement new functions on it. This means you can have a lot of functions defined on a basic data type which is amazing for composition but you can't add a new type that works with the same methods if you didn't anticipate this need.
http://homepages.inf.ed.ac.uk/wadler/papers/expression/expre...
http://stackoverflow.com/a/2079678 is a great SO answer on this topic.
Video: https://www.infoq.com/presentations/object-algebras
Paper: https://www.cs.utexas.edu/~wcook/Drafts/2012/ecoop2012.pdf
I understand that there is a comparable solution in FP languages called finally tagless interpreters: https://oleksandrmanzyuk.wordpress.com/2014/06/18/from-objec...
Speaking of parametric polymorphism, the need to modify a type's behaviour by implementing a new type is alleviated if you go with higher-kinded polymorphism, where the implementation bits are abstracted by a generic F[_] type and using type classes to go along with that.
In the example I'm giving in that presentation, I'm implementing a type named Iterant, for which the plugged-in F[_] can dramatically modify its behaviour. So in practice you don't need to implement a new kind of Iterant, which wouldn't make much sense anyway, you only need to implement a new F[_], which is used to abstract away the details of how Iterant gets evaluated, which is the part that people want to change.
Unfortunately most statically typed mainstream languages are not capable of expressing such abstractions due to lack of higher kinded types, or ways to encode / express type-classes, although this part is less problematic than lack of HKTs.