By comparison, you really see a lot more of the utility of OO in languages smalltalk or possibly ruby[2] where you can extend everything. I know tend to write my ruby (despite it being a multi-paradigm language) in a manner that you describe: FP style with objects hiding the details.
Of course, all of these languages have their strengths and weaknesses and OO isn't useful for everything. I just think OO has gotten a bit of a bad reputation from some of the languages that chose to label themselves OO even when their implementation was only superficial. This bad reputation may lead to dismissal of the whole idea, producing the false dichotomy you mention.
Incidentally, the lack of strict OO (or any language style) in ruby is what I really like about the language. You can be strict OO if you want, but you can also use classic (C-style) imperative programing when it makes more sense (or FP, or whatever).
[1] http://c2.com/cgi/wiki?AlanKaysDefinitionOfObjectOriented
[2] Regrettably, OCaml is one of those languages that is still in my "looks interesting, I should learn that" queue, so I cannot speak to how it implements OO.