OOP vs Functional Programming vs Procedural
All of them are good in their own ways - They're simply different approaches to the same problems.
In a purely procedural style, data tends to be highly decoupled from the functions that operate on it.
In an object oriented style, data tends to carry with it a collection of functions.
In a functional style, data and functions tend toward having more in common with each other (as in Lisp and Scheme) while offering more flexibility in terms of how functions are actually used. Algorithms tend also to be defined in terms of recursion and composition rather than loops and iteration.
Of course, the language itself only influences which style is preferred. Even in a pure-functional language like Haskell, you can write in a procedural style (though that is highly discouraged), and even in a procedural language like C, you can program in an object-oriented style (such as in the GTK+ and EFL APIs).
To be clear, the "advantage" of each paradigm is simply in the modeling of your algorithms and data structures. If, for example, your algorithm involves lists and trees, a functional algorithm may be the most sensible. Or, if, for example, your data is highly structured, it may make more sense to compose it as objects if that is the native paradigm of your language - or, it could just as easily be written as a functional abstraction of monads, which is the native paradigm of languages like Haskell or ML.
The choice of which you use is simply what makes more sense for your project and the abstractions your language supports.
I think the available libraries, tools, examples, and communities completely trumps the paradigm these days. For example, ML (or whatever) might be the ultimate all-purpose programming language but if you can't get any good libraries for what you are doing you're screwed.
For example, if you're making a video game, there are more good code examples and SDKs in C++, so you're probably better off with that. For a small web application, there are some great Python, PHP, and Ruby frameworks that'll get you off and running very quickly. Java is a great choice for larger projects because of the compile-time checking and enterprise libraries and platforms.
It used to be the case that the standard libraries for different languages were pretty small and easily replicated - C, C++, Assembler, ML, LISP, etc.. came with the basics, but tended to chicken out when it came to standardizing on things like network communications, encryption, graphics, data file formats (including XML), even basic data structures like balanced trees and hashtables were left out!
Modern languages like Python, PHP, Ruby, and Java now come with a far more decent standard library and have many good third party libraries you can easily use, thanks in great part to their adoption of namespaces to keep libraries from colliding with one another, and garbage collection to standardize the memory management schemes of the libraries.
These paradigms don't have to be mutually exclusive. If you look at python, it supports functions and classes, but at the same time, everything is an object, including functions. You can mix and match functional/oop/procedural style all in one piece of code.
What I mean is, in functional languages (at least in Haskell, the only one I studied) there are no statements! functions are only allowed one expression inside them!! BUT, functions are first-class citizens, you can pass them around as parameters, along with a bunch of other abilities. They can do powerful things with few lines of code.
While in a procedural language like C, the only way you can pass functions around is by using function pointers, and that alone doesn't enable many powerful tasks.
In python, a function is a first-class citizen, but it can contain arbitrary number of statements. So you can have a function that contains procedural code, but you can pass it around just like functional languages.
Same goes for OOP. A language like Java doesn't allow you to write procedures/functions outside of a class. The only way to pass a function around is to wrap it in an object that implements that function, and then pass that object around.
In Python, you don't have this restriction.
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